# American Institute of Mathematical Sciences

February  2016, 9(1): iii-ix. doi: 10.3934/dcdss.2016.9.1iii

## The research of Paolo Secchi

 1 Department of Mathematics, Pisa University, Via F.Buonarroti, 1, 56127-Pisa, Italy 2 DICATAM, Sezione di Matematica, Università di Brescia, Via Valotti, 9, 25133 Brescia 3 Dipartimento di Matematica, Università di Brescia, Facoltà di Ingegneria, Via Valotti 9, 25133 Brescia

Published  December 2015

The research of Professor Paolo Secchi concerns the theory of partial differential equations, especially from fluid dynamics.

Citation: Hugo Beirão da Veiga, Alessandro Morando, Paola Trebeschi. The research of Paolo Secchi. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : iii-ix. doi: 10.3934/dcdss.2016.9.1iii
##### References:
 [1] P. Secchi, On the initial value problem for the equation of motion of viscous incompressible fluids in the presence of diffusion,, Boll. UMI B (6), 1 (1982), 1117. Google Scholar [2] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids,, J. Reine Angew. Math., 341 (1983), 1. doi: 10.1515/crll.1983.341.1. Google Scholar [3] P. Secchi, Existence theorems for compressible viscous fluids having zero shear viscosity,, Rend. Sem. Mat. Univ. Padova, 71 (1984), 73. Google Scholar [4] V. Casulli, G. Pontrelli and P. Secchi, An Eulerian-Lagrangian method for open channel flows,, in Numerical Methods in Laminar and Turbulent Flow, (1985), 1360. Google Scholar [5] P. Secchi, Flussi non stazionari di fluidi incompressibili viscosi e ideali in un semipiano,, Ricerche di Matematica, 34 (1985), 27. Google Scholar [6] H. Beirão da Veiga and P. Secchi, $L^p$-stability for the strong solutions of the Navier-Stokes equations in the whole space,, Arch. Rat. Mech. Anal., 98 (1987), 65. doi: 10.1007/BF00279962. Google Scholar [7] P. Secchi, $L^2$-stability for weak solutions of the Navier-Stokes equations in $\mathbbR^3$,, Indiana Univ. Math. J., 36 (1987), 685. doi: 10.1512/iumj.1987.36.36039. Google Scholar [8] P. Marcati, A. J. Milani and P. Secchi, Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system,, Manuscripta Mathematica, 60 (1988), 49. doi: 10.1007/BF01168147. Google Scholar [9] P. Secchi, On the motion of viscous fluids in the presence of diffusion,, SIAM J. on Math. Anal., 19 (1988), 22. doi: 10.1137/0519002. Google Scholar [10] P. Secchi, On the stationary and nonstationary Navier-Stokes equations in $\mathbbR^n$,, Ann. Mat. Pura Appl. (IV), 153 (1988), 293. doi: 10.1007/BF01762396. Google Scholar [11] P. Secchi, A note on the generic solvability of the Navier-Stokes equations,, Rend. Sem. Mat. Univ. Padova, 83 (1990), 177. Google Scholar [12] P. Secchi, On the motion of gaseous stars in the presence of radiation,, Comm. P.D.E., 15 (1990), 185. doi: 10.1080/03605309908820683. Google Scholar [13] P. Secchi, On the uniqueness of motion of viscous gaseous stars,, Math. Methods Appl. Sci., 13 (1990), 391. doi: 10.1002/mma.1670130504. Google Scholar [14] P. Secchi, On the evolution equations of viscous gaseous stars,, Ann. Scuola Norm. Sup. Pisa, 18 (1991), 295. Google Scholar [15] P. Secchi, On nonviscous compressible fluids in a time-dependent domain,, Ann. Inst. Henri Poincaré, 9 (1992), 683. Google Scholar [16] P. Secchi, On the motion of nonviscous compressible fluids in domains with boundary,, Partial Differential Equations, 27 (1992), 447. Google Scholar [17] P. Secchi, On the equations of ideal incompressible magneto-hydrodynamics,, Rend. Sem. Mat. Univ. Padova, 90 (1993), 103. Google Scholar [18] P. Secchi, Mixed problems for linear symmetric hyperbolic systems with characteristic boundary condition,, in Qualitative Aspects and Applications of Nonlinear Evolution Equations (Trieste, (1993), 88. Google Scholar [19] P. Secchi, On a stationary problem for the compressible Navier-Stokes equations,, Differential Integral Equations, 7 (1994), 463. Google Scholar [20] P. Secchi, On the stationary motion of compressible viscous fluids,, Ann. Scuola Norm. Sup. Pisa, 21 (1994), 131. Google Scholar [21] P. Secchi, Linear symmetric hyperbolic systems with characteristic boundary,, Math. Methods Appl. Sci., 18 (1995), 855. doi: 10.1002/mma.1670181103. Google Scholar [22] P. Secchi, On an initial boundary value problem for the equations of ideal magneto-hydrodynamics,, Math. Methods Appl. Sci., 18 (1995), 841. doi: 10.1002/mma.1670181102. Google Scholar [23] P. Secchi, On nonviscous compressible fluids in domains with moving boundaries,, in Nonlinear Variational Problems and Partial Differential Equations (Isola d'Elba, (1990), 229. Google Scholar [24] P. Secchi, Well-posedness for a mixed problem for the equations of ideal magneto-hydrodynamics,, Archiv Math. (Basel), 64 (1995), 237. doi: 10.1007/BF01188574. Google Scholar [25] P. Secchi, The initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity,, Differential Integral Equations, 9 (1996), 671. Google Scholar [26] P. Secchi, Well-posedness of characteristic symmetric hyperbolic systems,, Arch. Rat. Mech. Anal., 134 (1996), 155. doi: 10.1007/BF00379552. Google Scholar [27] P. Secchi, Characteristic symmetric hyperbolic systems with dissipation: Global existence and asymptotics,, Math. Methods Appl. Sci., 20 (1997), 583. doi: 10.1002/(SICI)1099-1476(19970510)20:7<583::AID-MMA865>3.0.CO;2-T. Google Scholar [28] F. Gazzola and P. Secchi, Some results about stationary Navier-Stokes equations with a pressure-dependent viscosity,, in Navier-Stokes Equations: Theory and Numerical Methods (Varenna, (1997), 31. Google Scholar [29] P. Secchi, Inflow-outflow problems for inviscid compressible fluids,, Commun. Appl. Anal., 2 (1998), 81. Google Scholar [30] P. Secchi, The open boundary problem for inviscid compressible fluids,, in Navier-Stokes Equations and Related Nonlinear Problems (Palanga, (1997), 279. Google Scholar [31] P. Secchi, A symmetric positive system with nonuniformly characteristic boundary,, Differential Integral Equations, 11 (1998), 605. Google Scholar [32] P. Secchi, Full regularity of solutions to a nonuniformly characteristic boundary value problem for symmetric positive systems,, Adv. Math. Sci. Appl., 10 (2000), 39. Google Scholar [33] P. Secchi, On the incompressible limit of inviscid compressible fluids,, Ann. Univ. Ferrara Sez. VII (N.S.), 46 (2000), 21. Google Scholar [34] P. Secchi, On the singular incompressible limit of inviscid compressible fluids,, J. Math. Fluid Mech., 2 (2000), 107. doi: 10.1007/PL00000948. Google Scholar [35] P. Secchi, Some properties of anisotropic sobolev spaces,, Archiv Math. (Basel), 75 (2000), 207. doi: 10.1007/s000130050494. Google Scholar [36] F. Gazzola and P. Secchi, Inflow-outflow problems for euler equations in a rectangular domain,, NoDEA, 8 (2001), 195. doi: 10.1007/PL00001445. Google Scholar [37] E. Casella, P. Secchi and P. Trebeschi, Global existence of 2D slightly compressible viscous magneto-fluid motion,, Portugaliae Mathematica, 59 (2002), 67. Google Scholar [38] P. Secchi, An initial boundary value problem in ideal magneto-hydrodynamics,, NoDEA, 9 (2002), 441. doi: 10.1007/PL00012608. Google Scholar [39] P. Secchi, Life span and global existence of 2-D compressible fluids,, in The Navier-Stokes Equations: Theory and Numerical Methods (Varenna, (2000), 99. Google Scholar [40] P. Secchi, Life span of 2-D irrotational compressible fluids in the halfplane,, Math. Methods Appl. Sci., 25 (2002), 895. doi: 10.1002/mma.318. Google Scholar [41] P. Secchi, On slightly compressible ideal flow in the halfplane,, Arch. Rat. Mech. Anal., 161 (2002), 231. doi: 10.1007/s002050100179. Google Scholar [42] P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation II,, Rend. Sem. Mat. Univ. Padova, 108 (2002), 67. Google Scholar [43] E. Casella, P. Secchi and P. Trebeschi, Global classical solutions of 2D MHD system,, J. Math. Fluid Mech., 5 (2003), 70. doi: 10.1007/s000210300003. Google Scholar [44] P. Secchi and Y. Shibata, On the decay of solutions to the 2D Neumann exterior problem for the wave equation,, J. Differential Equations, 194 (2003), 221. doi: 10.1016/S0022-0396(03)00189-X. Google Scholar [45] J.-F. Coulombel and P. Secchi, On the transition to instability for compressible vortex sheets,, Proc. Roy. Soc. Edinburgh, 134 (2004), 885. doi: 10.1017/S0308210500003528. Google Scholar [46] J.-F. Coulombel and P. Secchi, The stability of compressible vortex sheets in two space dimensions,, Indiana Univ. Math. J., 53 (2004), 941. doi: 10.1512/iumj.2004.53.2526. Google Scholar [47] A. Morando and P. Secchi, On 3D slightly compressible Euler equations,, Portugaliae Mathematica, 61 (2004), 301. Google Scholar [48] P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation,, Boll. UMI B (8), 7 (2004), 189. Google Scholar [49] J.-F. Coulombel and P. Secchi, Stability of compressible vortex sheets,, in EQUADIFF 2003, (2003), 502. doi: 10.1142/9789812702067_0081. Google Scholar [50] P. Secchi, On compressible vortex sheets,, J. Math. Fluid Mech., 7 (2005). doi: 10.1007/s00021-005-0158-6. Google Scholar [51] P. Secchi and P. Trebeschi, Non-homogeneous quasi-linear symmetric hyperbolic systems with characteristic boundary,, Int. J. Pure Appl. Math., 23 (2005), 39. Google Scholar [52] E. Casella, P. Secchi and P. Trebeschi, Non-homogeneous linear symmetric hyperbolic systems with characteristic boundary,, Differential Integral Equations, 19 (2006), 51. Google Scholar [53] P. Secchi, 2D slightly compressible ideal flow in an exterior domain,, J. Math. Fluid Mech., 8 (2006), 564. doi: 10.1007/s00021-005-0188-0. Google Scholar [54] P. Secchi, On compressible and incompressible vortex sheets,, in Analysis and Simulation of Fluid Dynamics, (2007), 201. doi: 10.1007/978-3-7643-7742-7_12. Google Scholar [55] J.-F. Coulombel and P. Secchi, Nonlinear compressible vortex sheets in two space dimensions,, Ann. Sci. Éc. Norm. Supér. (4), 41 (2008), 85. Google Scholar [56] J.-F. Coulombel and P. Secchi, Nonlinear stability of compressible vortex sheets,, in Hyperbolic Problems: Theory, (2008), 415. doi: 10.1007/978-3-540-75712-2_38. Google Scholar [57] J.-F. Coulombel and P. Secchi, Uniqueness of 2-D compressible vortex sheets,, Comm. Pure Appl. Anal., 8 (2009), 1439. doi: 10.3934/cpaa.2009.8.1439. Google Scholar [58] A. Morando, P. Secchi and P. Trebeschi, Characteristic initial boundary value problems for symmetrizable systems,, Rend. Semin. Mat. Univ. Politec. Torino, 67 (2009), 229. Google Scholar [59] A. Morando, P. Secchi and P. Trebeschi, Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems,, J. Hyperbolic Differ. Equ., 6 (2009), 753. doi: 10.1142/S021989160900199X. Google Scholar [60] P. Secchi, A. Morando and P. Trebeschi, Hyperbolic problems with characteristic boundary,, in Qualitative Properties of Solutions to Partial Differential Equations, (2009), 135. Google Scholar [61] D. Catania and P. Secchi, Global existence and finite dimensional global attractor for a 3D double viscous MHD-alpha model,, Commun. Math. Sci., 8 (2010), 1021. doi: 10.4310/CMS.2010.v8.n4.a12. Google Scholar [62] A. Morando and P. Secchi, Regularity of weakly well-posed characteristic boundary value problems,, Int. J. Differ. Equ., (2010). Google Scholar [63] P. Secchi, An alpha model for compressible fluids,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 351. doi: 10.3934/dcdss.2010.3.351. Google Scholar [64] D. Catania and P. Secchi, Global existence for two regularized MHD models in three space-dimension,, Portugaliae Mathematica, 68 (2011), 41. doi: 10.4171/PM/1880. Google Scholar [65] A. Morando and P. Secchi, Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary,, J. Hyperbolic Differ. Equ., 8 (2011), 37. doi: 10.1142/S021989161100238X. Google Scholar [66] D. Catania and P. Secchi, Global regularity for some MHD-alpha systems,, Riv. Mat. Univ. Parma, 3 (2012), 25. Google Scholar [67] J.-F. Coulombel, A. Morando, P. Secchi and P. Trebeschi, A priori estimates for 3D incompressible current-vortex sheets,, Commun. Math. Phys., 311 (2012), 247. doi: 10.1007/s00220-011-1340-8. Google Scholar [68] A. Morando and P. Secchi, Weakly well posed characteristic hyperbolic problems,, Riv. Mat. Univ. Parma, 3 (2012), 147. Google Scholar [69] P. Secchi, A higher-order Hardy-type inequality in anisotropic Sobolev spaces,, Int. J. Differ. Equ., (2012). Google Scholar [70] P. Secchi and Y. Trakhinin, Well-posedness of the linearized plasma-vacuum interface problem,, Interfaces and Free Boundaries, 15 (2013), 323. doi: 10.4171/IFB/305. Google Scholar [71] D. Catania, M. D'Abbicco and P. Secchi, Stability of the linearized MHD-Maxwell free interface problem,, Comm. Pure Appl. Anal., 13 (2014), 2407. doi: 10.3934/cpaa.2014.13.2407. Google Scholar [72] A. Morando, P. Secchi and P. Trebeschi, On a priori energy estimates for characteristic boundary value problems,, J. Fourier Anal. Appl., 20 (2014), 816. doi: 10.1007/s00041-014-9335-4. Google Scholar [73] P. Secchi and Y. Trakhinin, Well-posedness of the plasma-vacuum interface problem,, Nonlinearity, 27 (2014), 105. doi: 10.1088/0951-7715/27/1/105. Google Scholar [74] P. Secchi, Nonlinear surface waves on the plasma-vacuum interface,, Quart. Appl. Math., (2015). doi: 10.1090/qam/1405. Google Scholar [75] P. Secchi, On the Nash-Moser iteration technique,, in Recent Developments of Mathematical Fluid Mechanics, (). Google Scholar

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##### References:
 [1] P. Secchi, On the initial value problem for the equation of motion of viscous incompressible fluids in the presence of diffusion,, Boll. UMI B (6), 1 (1982), 1117. Google Scholar [2] P. Secchi and A. Valli, A free boundary problem for compressible viscous fluids,, J. Reine Angew. Math., 341 (1983), 1. doi: 10.1515/crll.1983.341.1. Google Scholar [3] P. Secchi, Existence theorems for compressible viscous fluids having zero shear viscosity,, Rend. Sem. Mat. Univ. Padova, 71 (1984), 73. Google Scholar [4] V. Casulli, G. Pontrelli and P. Secchi, An Eulerian-Lagrangian method for open channel flows,, in Numerical Methods in Laminar and Turbulent Flow, (1985), 1360. Google Scholar [5] P. Secchi, Flussi non stazionari di fluidi incompressibili viscosi e ideali in un semipiano,, Ricerche di Matematica, 34 (1985), 27. Google Scholar [6] H. Beirão da Veiga and P. Secchi, $L^p$-stability for the strong solutions of the Navier-Stokes equations in the whole space,, Arch. Rat. Mech. Anal., 98 (1987), 65. doi: 10.1007/BF00279962. Google Scholar [7] P. Secchi, $L^2$-stability for weak solutions of the Navier-Stokes equations in $\mathbbR^3$,, Indiana Univ. Math. J., 36 (1987), 685. doi: 10.1512/iumj.1987.36.36039. Google Scholar [8] P. Marcati, A. J. Milani and P. Secchi, Singular convergence of weak solutions for a quasilinear nonhomogeneous hyperbolic system,, Manuscripta Mathematica, 60 (1988), 49. doi: 10.1007/BF01168147. Google Scholar [9] P. Secchi, On the motion of viscous fluids in the presence of diffusion,, SIAM J. on Math. Anal., 19 (1988), 22. doi: 10.1137/0519002. Google Scholar [10] P. Secchi, On the stationary and nonstationary Navier-Stokes equations in $\mathbbR^n$,, Ann. Mat. Pura Appl. (IV), 153 (1988), 293. doi: 10.1007/BF01762396. Google Scholar [11] P. Secchi, A note on the generic solvability of the Navier-Stokes equations,, Rend. Sem. Mat. Univ. Padova, 83 (1990), 177. Google Scholar [12] P. Secchi, On the motion of gaseous stars in the presence of radiation,, Comm. P.D.E., 15 (1990), 185. doi: 10.1080/03605309908820683. Google Scholar [13] P. Secchi, On the uniqueness of motion of viscous gaseous stars,, Math. Methods Appl. Sci., 13 (1990), 391. doi: 10.1002/mma.1670130504. Google Scholar [14] P. Secchi, On the evolution equations of viscous gaseous stars,, Ann. Scuola Norm. Sup. Pisa, 18 (1991), 295. Google Scholar [15] P. Secchi, On nonviscous compressible fluids in a time-dependent domain,, Ann. Inst. Henri Poincaré, 9 (1992), 683. Google Scholar [16] P. Secchi, On the motion of nonviscous compressible fluids in domains with boundary,, Partial Differential Equations, 27 (1992), 447. Google Scholar [17] P. Secchi, On the equations of ideal incompressible magneto-hydrodynamics,, Rend. Sem. Mat. Univ. Padova, 90 (1993), 103. Google Scholar [18] P. Secchi, Mixed problems for linear symmetric hyperbolic systems with characteristic boundary condition,, in Qualitative Aspects and Applications of Nonlinear Evolution Equations (Trieste, (1993), 88. Google Scholar [19] P. Secchi, On a stationary problem for the compressible Navier-Stokes equations,, Differential Integral Equations, 7 (1994), 463. Google Scholar [20] P. Secchi, On the stationary motion of compressible viscous fluids,, Ann. Scuola Norm. Sup. Pisa, 21 (1994), 131. Google Scholar [21] P. Secchi, Linear symmetric hyperbolic systems with characteristic boundary,, Math. Methods Appl. Sci., 18 (1995), 855. doi: 10.1002/mma.1670181103. Google Scholar [22] P. Secchi, On an initial boundary value problem for the equations of ideal magneto-hydrodynamics,, Math. Methods Appl. Sci., 18 (1995), 841. doi: 10.1002/mma.1670181102. Google Scholar [23] P. Secchi, On nonviscous compressible fluids in domains with moving boundaries,, in Nonlinear Variational Problems and Partial Differential Equations (Isola d'Elba, (1990), 229. Google Scholar [24] P. Secchi, Well-posedness for a mixed problem for the equations of ideal magneto-hydrodynamics,, Archiv Math. (Basel), 64 (1995), 237. doi: 10.1007/BF01188574. Google Scholar [25] P. Secchi, The initial boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity,, Differential Integral Equations, 9 (1996), 671. Google Scholar [26] P. Secchi, Well-posedness of characteristic symmetric hyperbolic systems,, Arch. Rat. Mech. Anal., 134 (1996), 155. doi: 10.1007/BF00379552. Google Scholar [27] P. Secchi, Characteristic symmetric hyperbolic systems with dissipation: Global existence and asymptotics,, Math. Methods Appl. Sci., 20 (1997), 583. doi: 10.1002/(SICI)1099-1476(19970510)20:7<583::AID-MMA865>3.0.CO;2-T. Google Scholar [28] F. Gazzola and P. Secchi, Some results about stationary Navier-Stokes equations with a pressure-dependent viscosity,, in Navier-Stokes Equations: Theory and Numerical Methods (Varenna, (1997), 31. Google Scholar [29] P. Secchi, Inflow-outflow problems for inviscid compressible fluids,, Commun. Appl. Anal., 2 (1998), 81. Google Scholar [30] P. Secchi, The open boundary problem for inviscid compressible fluids,, in Navier-Stokes Equations and Related Nonlinear Problems (Palanga, (1997), 279. Google Scholar [31] P. Secchi, A symmetric positive system with nonuniformly characteristic boundary,, Differential Integral Equations, 11 (1998), 605. Google Scholar [32] P. Secchi, Full regularity of solutions to a nonuniformly characteristic boundary value problem for symmetric positive systems,, Adv. Math. Sci. Appl., 10 (2000), 39. Google Scholar [33] P. Secchi, On the incompressible limit of inviscid compressible fluids,, Ann. Univ. Ferrara Sez. VII (N.S.), 46 (2000), 21. Google Scholar [34] P. Secchi, On the singular incompressible limit of inviscid compressible fluids,, J. Math. Fluid Mech., 2 (2000), 107. doi: 10.1007/PL00000948. Google Scholar [35] P. Secchi, Some properties of anisotropic sobolev spaces,, Archiv Math. (Basel), 75 (2000), 207. doi: 10.1007/s000130050494. Google Scholar [36] F. Gazzola and P. Secchi, Inflow-outflow problems for euler equations in a rectangular domain,, NoDEA, 8 (2001), 195. doi: 10.1007/PL00001445. Google Scholar [37] E. Casella, P. Secchi and P. Trebeschi, Global existence of 2D slightly compressible viscous magneto-fluid motion,, Portugaliae Mathematica, 59 (2002), 67. Google Scholar [38] P. Secchi, An initial boundary value problem in ideal magneto-hydrodynamics,, NoDEA, 9 (2002), 441. doi: 10.1007/PL00012608. Google Scholar [39] P. Secchi, Life span and global existence of 2-D compressible fluids,, in The Navier-Stokes Equations: Theory and Numerical Methods (Varenna, (2000), 99. Google Scholar [40] P. Secchi, Life span of 2-D irrotational compressible fluids in the halfplane,, Math. Methods Appl. Sci., 25 (2002), 895. doi: 10.1002/mma.318. Google Scholar [41] P. Secchi, On slightly compressible ideal flow in the halfplane,, Arch. Rat. Mech. Anal., 161 (2002), 231. doi: 10.1007/s002050100179. Google Scholar [42] P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation II,, Rend. Sem. Mat. Univ. Padova, 108 (2002), 67. Google Scholar [43] E. Casella, P. Secchi and P. Trebeschi, Global classical solutions of 2D MHD system,, J. Math. Fluid Mech., 5 (2003), 70. doi: 10.1007/s000210300003. Google Scholar [44] P. Secchi and Y. Shibata, On the decay of solutions to the 2D Neumann exterior problem for the wave equation,, J. Differential Equations, 194 (2003), 221. doi: 10.1016/S0022-0396(03)00189-X. Google Scholar [45] J.-F. Coulombel and P. Secchi, On the transition to instability for compressible vortex sheets,, Proc. Roy. Soc. Edinburgh, 134 (2004), 885. doi: 10.1017/S0308210500003528. Google Scholar [46] J.-F. Coulombel and P. Secchi, The stability of compressible vortex sheets in two space dimensions,, Indiana Univ. Math. J., 53 (2004), 941. doi: 10.1512/iumj.2004.53.2526. Google Scholar [47] A. Morando and P. Secchi, On 3D slightly compressible Euler equations,, Portugaliae Mathematica, 61 (2004), 301. Google Scholar [48] P. Secchi, Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation,, Boll. UMI B (8), 7 (2004), 189. Google Scholar [49] J.-F. Coulombel and P. Secchi, Stability of compressible vortex sheets,, in EQUADIFF 2003, (2003), 502. doi: 10.1142/9789812702067_0081. Google Scholar [50] P. Secchi, On compressible vortex sheets,, J. Math. Fluid Mech., 7 (2005). doi: 10.1007/s00021-005-0158-6. Google Scholar [51] P. Secchi and P. Trebeschi, Non-homogeneous quasi-linear symmetric hyperbolic systems with characteristic boundary,, Int. J. Pure Appl. Math., 23 (2005), 39. Google Scholar [52] E. Casella, P. Secchi and P. Trebeschi, Non-homogeneous linear symmetric hyperbolic systems with characteristic boundary,, Differential Integral Equations, 19 (2006), 51. Google Scholar [53] P. Secchi, 2D slightly compressible ideal flow in an exterior domain,, J. Math. Fluid Mech., 8 (2006), 564. doi: 10.1007/s00021-005-0188-0. Google Scholar [54] P. Secchi, On compressible and incompressible vortex sheets,, in Analysis and Simulation of Fluid Dynamics, (2007), 201. doi: 10.1007/978-3-7643-7742-7_12. Google Scholar [55] J.-F. Coulombel and P. Secchi, Nonlinear compressible vortex sheets in two space dimensions,, Ann. Sci. Éc. Norm. Supér. (4), 41 (2008), 85. Google Scholar [56] J.-F. Coulombel and P. Secchi, Nonlinear stability of compressible vortex sheets,, in Hyperbolic Problems: Theory, (2008), 415. doi: 10.1007/978-3-540-75712-2_38. Google Scholar [57] J.-F. Coulombel and P. Secchi, Uniqueness of 2-D compressible vortex sheets,, Comm. Pure Appl. Anal., 8 (2009), 1439. doi: 10.3934/cpaa.2009.8.1439. Google Scholar [58] A. Morando, P. Secchi and P. Trebeschi, Characteristic initial boundary value problems for symmetrizable systems,, Rend. Semin. Mat. Univ. Politec. Torino, 67 (2009), 229. Google Scholar [59] A. Morando, P. Secchi and P. Trebeschi, Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems,, J. Hyperbolic Differ. Equ., 6 (2009), 753. doi: 10.1142/S021989160900199X. Google Scholar [60] P. Secchi, A. Morando and P. Trebeschi, Hyperbolic problems with characteristic boundary,, in Qualitative Properties of Solutions to Partial Differential Equations, (2009), 135. Google Scholar [61] D. Catania and P. Secchi, Global existence and finite dimensional global attractor for a 3D double viscous MHD-alpha model,, Commun. Math. Sci., 8 (2010), 1021. doi: 10.4310/CMS.2010.v8.n4.a12. Google Scholar [62] A. Morando and P. Secchi, Regularity of weakly well-posed characteristic boundary value problems,, Int. J. Differ. Equ., (2010). Google Scholar [63] P. Secchi, An alpha model for compressible fluids,, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), 351. doi: 10.3934/dcdss.2010.3.351. Google Scholar [64] D. Catania and P. Secchi, Global existence for two regularized MHD models in three space-dimension,, Portugaliae Mathematica, 68 (2011), 41. doi: 10.4171/PM/1880. Google Scholar [65] A. Morando and P. Secchi, Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary,, J. Hyperbolic Differ. Equ., 8 (2011), 37. doi: 10.1142/S021989161100238X. Google Scholar [66] D. Catania and P. Secchi, Global regularity for some MHD-alpha systems,, Riv. Mat. Univ. Parma, 3 (2012), 25. Google Scholar [67] J.-F. Coulombel, A. Morando, P. Secchi and P. Trebeschi, A priori estimates for 3D incompressible current-vortex sheets,, Commun. Math. Phys., 311 (2012), 247. doi: 10.1007/s00220-011-1340-8. Google Scholar [68] A. Morando and P. Secchi, Weakly well posed characteristic hyperbolic problems,, Riv. Mat. Univ. Parma, 3 (2012), 147. Google Scholar [69] P. Secchi, A higher-order Hardy-type inequality in anisotropic Sobolev spaces,, Int. J. Differ. Equ., (2012). Google Scholar [70] P. Secchi and Y. Trakhinin, Well-posedness of the linearized plasma-vacuum interface problem,, Interfaces and Free Boundaries, 15 (2013), 323. doi: 10.4171/IFB/305. Google Scholar [71] D. Catania, M. D'Abbicco and P. Secchi, Stability of the linearized MHD-Maxwell free interface problem,, Comm. Pure Appl. Anal., 13 (2014), 2407. doi: 10.3934/cpaa.2014.13.2407. Google Scholar [72] A. Morando, P. Secchi and P. Trebeschi, On a priori energy estimates for characteristic boundary value problems,, J. Fourier Anal. Appl., 20 (2014), 816. doi: 10.1007/s00041-014-9335-4. Google Scholar [73] P. Secchi and Y. Trakhinin, Well-posedness of the plasma-vacuum interface problem,, Nonlinearity, 27 (2014), 105. doi: 10.1088/0951-7715/27/1/105. Google Scholar [74] P. Secchi, Nonlinear surface waves on the plasma-vacuum interface,, Quart. Appl. Math., (2015). doi: 10.1090/qam/1405. Google Scholar [75] P. Secchi, On the Nash-Moser iteration technique,, in Recent Developments of Mathematical Fluid Mechanics, (). Google Scholar
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