1. Uniqueness of the solution to the 2D Vlasov–Navier–Stokes system
- Author
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Daniel Han-Kwan, Iván Moyano, Evelyne Miot, Ayman Moussa, Centre de Mathématiques Laurent Schwartz (CMLS), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Fourier (IF), and Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
- Subjects
General Mathematics ,010102 general mathematics ,Vlasov equation ,Context (language use) ,Function (mathematics) ,Space (mathematics) ,01 natural sciences ,Mathematics - Analysis of PDEs ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Order (group theory) ,Applied mathematics ,Maximal function ,Navier stokes ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
International audience; We prove a uniqueness result for weak solutions to the Vlasov-Navier-Stokes system in two dimensions, both in the whole space and in the periodic case, under a mild decay condition on the initial distribution function. The main result is achieved by combining methods from optimal transportation (introduced in this context by G. Loeper) with the use of Hardy's maximal function, in order to obtain some fine Wassestein-like estimates for the difference of two solutions of the Vlasov equation.
- Published
- 2019
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