Uniqueness of the solution to the 2D Vlasov–Navier–Stokes system

• Daniel Han-Kwan ^[1] ; Évelyne Miot ^[2] ; Ayman Moussa ^[3] ; Iván Moyano ^[4]
  1. [1] École Polytechnique

     École Polytechnique

     Arrondissement de Palaiseau, Francia

     
  2. [2] Grenoble Alpes University

     Grenoble Alpes University

     Arrondissement de Grenoble, Francia

     
  3. [3] Université Denis Diderot

     Université Denis Diderot

     París, Francia

     
  4. [4] University of Cambridge

     University of Cambridge

     Cambridge District, Reino Unido

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 1, 2020, págs. 37-60
• Idioma: inglés
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• Resumen

  • 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 Wasserstein-like estimates for the difference of two solutions of the Vlasov equation.