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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Flows of vector fields with point singularities and the vortex-wave system
Pages: 2405 - 2417, Issue 5, May 2016

doi:10.3934/dcds.2016.36.2405      Abstract        References        Full text (412.9K)           Related Articles

Gianluca Crippa - Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, 4051 Basel, Switzerland (email)
Milton C. Lopes Filho - Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil (email)
Evelyne Miot - Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz, 91128 Palaiseau, France (email)
Helena J. Nussenzveig Lopes - Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ, Brazil (email)

1 L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, Invent. Math., 158 (2004), 227-260.       
2 L. Ambrosio, Transport equation and Cauchy problem for non-smooth vector fields, in Calculus of Variations and Nonlinear Partial Differential Equations, Lecture Notes in Math., 1927, Springer, Berlin, 2008, 1-41.       
3 L. Ambrosio and G. Crippa, Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields, in Transport Equations and Multi-D Hyperbolic Conservation Laws, Lecture Notes of the Unione Matematica Italiana, 5, Springer, Berlin, 2008, 3-57.       
4 L. Ambrosio and G. Crippa, Continuity equations and ODE flows with non-smooth velocity, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 144 (2014), 1191-1244.       
5 F. Bouchut and G. Crippa, Lagrangian flows for vector fields with gradient given by a singular integral, J. Hyper. Differential Equations, 10 (2013), 235-282.       
6 S. Caprino, C. Marchioro, E. Miot and M. Pulvirenti, On the attractive plasma-charge system in 2-d, Comm. Partial Differential Equations, 37 (2012), 1237-1272.       
7 G. Crippa and C. De Lellis, Estimates and regularity results for the DiPerna-Lions flow, J. Reine Angew. Math., 616 (2008), 15-46.       
8 R. J. DiPerna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98 (1989), 511-547.       
9 D. Jin and D. Dubin, Point vortex dynamics within a background vorticity patch, Phys. Fluids, 13 (2001), 677-691.       
10 M. C. Lopes Filho, E. Miot and H. J. Nussenzveig Lopes, Existence of a weak solution in $L^p$ to the vortex-wave system, J. Nonlinear Science, 21 (2011), 685-703.       
11 M. C. Lopes Filho and H. J. Nussenzveig Lopes, An extension of Marchioro's bound on the growth of a vortex patch to flows with $L^p$ vorticity, SIAM J. Math. Anal., 29 (1998), 596-599 (electronic).       
12 C. Lacave and E. Miot, Uniqueness for the vortex-wave system when the vorticity is constant near the point vortex, SIAM J. Math. Anal., 41 (2009), 1138-1163.       
13 A. J. Majda and A. L. Bertozzi, Vorticity and Incompressible Flow, Cambridge Texts in Applied Mathematics, {27}, Cambridge University Press, Cambridge, 2002.       
14 C. Marchioro and M. Pulvirenti, On the vortex-wave system, in Mechanics, Analysis, and Geometry: 200 Years after Lagrange, Elsevier Science, Amsterdam, 1991, 79-95.       
15 C. Marchioro and M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, Springer-Verlag, New York, 1994.       
16 P. Newton, The N-vortex problem on a sphere: Geophysical mechanisms that break integrability, Theor. Comput. Fluid Dyn., 24 (2010), 137-149.
17 D. Schecter, Two-dimensional vortex dynamics with background vorticity, in CP606, Non-Neutral Plasma Physics IV, Vol. 606, American Institute of Physics, 2002, 443-452.
18 D. Schecter and D. Dubin, Theory and simulations of two-dimensional vortex motion driven by a background vorticity gradient, Phys. Fluids, 13 (2001), 1704-1723.
19 E. Stein, Harmonic Analysis, Princeton University Press, 1993.       

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