Communications on Pure and Applied Analysis (CPAA)

Infinite-energy solutions for the Navier-Stokes equations in a strip revisited
Pages: 1361 - 1393, Issue 4, July 2014

doi:10.3934/cpaa.2014.13.1361      Abstract        References        Full text (566.3K)           Related Articles

Peter Anthony - University of Surrey, Guildford, Gu27XH, Surrey, United Kingdom (email)
Sergey Zelik - Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom (email)

1 F. Abergel, Attractor for a Navier-Stokes flow in an unbounded domain. Attractors, inertial manifolds and their approximation (Marseille-Luminy, 1987). RAIRO Model. Math. Anal. Numer., 23 (1989), 359-370.       
2 F. Abergel, Existence and finite dimensionality of the global attractor for evolution equations on unbounded domains, J. Differential Equations, 83 (1990), 85-108.       
3 A. Afendikov and A. Mielke, Dynamical properties of spatially non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite strip, J. Math. Fluid Mech., 7 (2005), 51-67.       
4 H. Amann, On the strong solvability of the Navier-Stokes equations, Jour. Math.Fluid Mechanics, 2 (2000), 16-98.       
5 A. Babin, Asymptotic Expansions at infinity of a strongly perturbed Poiseuille flow, Advances in Soviet Math., 10 (1992), 1-83.       
6 A. Babin, The attractor of a Navier-Stokes system in an unbounded channel-like domain, J. Dynam. Differential Equations, 4 (1992), 555-584.       
7 A. Babin and M.Vishik, Attractors of partial differential evolution equations in an unbounded domain, Proc. Roy. Soc. Edinburgh Sect. A, 116 (1990), 221-243.       
8 A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, Nauka, Moscow, 1989; North Holland, Amsterdam, 1992.       
9 M. Efendiev and S. Zelik, The attractor for a nonlinear reaction-diffusion system in an unbounded domain, Comm. Pure Appl. Math., 54 (2001), 625-688.       
10 Y. Giga, S. Matsui and O. Sawada, Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity, J. Math. Fluid Mech., 3 (2001), 302-315.       
11 D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840. Springer-Verlag, Berlin-New York, 1981.       
12 P. Lemarie-Rieusset, Recent developments in the Navier-Stokes problem, Chapman $&$ Hall/CRC Research Notes in Mathematics, 431. Chapman & Hall/CRC, Boca Raton, FL, 2002.       
13 A. Mielke and G. Schneider, Attractors for modulation equations on unbounded domains - existence and comparison, Nonlinearity, 8 (1995), 743-768.       
14 A. Miranville and S. Zelik, Attractors for dissipative partial differential equations in bounded and unbounded domains, in Handbook of Differential Equations: Evolutionary Equations, Vol. IV, 103-200, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2008.       
15 J. Pennant and S. Zelik, Global well-posedness in uniformly local spaces for the Cahn-Hilliard equation in $\R^3$, Comm. Pure Appl. Anal., 12 (2013), 461-480.       
16 S. Revina and V. Yudovich, $L^p$-estimates for the resolvent of the Stokes operator in an infinite cylinder, (Russian) Mat. Sb., 187 (1996), 97-118; translation in Sb. Math., 187 (1996), 881-902.       
17 O. Sawada and Y. Taniuchi, A remark on $L^\infty$-solutions to the 2D Navier-Stokes equations, J. Math. Fluid Mech., 9 (2007), 533-542.       
18 R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam New York-Oxford, 1977.       
19 R. Temam, Infnite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematics Series, Springer, New York-Berlin, 1988; 2nd ed., New York, 1997.       
20 H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978.
21 S. Zelik, Spatially nondecaying solutions of the 2D Navier-Stokes equation in a strip, Glasg. Math. J., 49 (2007), 525-588.       
22 S. Zelik, Weak spatially nondecaying solutions of 3D Navier-Stokes equations in cylindrical domains, Instability in models connected with fluid flows. II, 255-327, Int. Math. Ser. (N. Y.), 7, Springer, New York, 2008.       
23 S. Zelik, Attractors of reaction-diffusion systems in unbounded domains and their spatial complexity, Comm. Pure Appl. Math., 56 (2003), 584-637.       
24 S. Zelik, Infinite energy solutions for damped Navier-Stokes equations in $\R^2$, Jour. Math. Fluid Mech., 15 (2013), 717-745.       

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