JournalsrmiVol. 36, No. 1pp. 37–60

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

  • Daniel Han-Kwan

    École Polytechnique, Palaiseau, France
  • Évelyne Miot

    Université Grenoble Alpes, Saint-Martin-d’Hères, France
  • Ayman Moussa

    Sorbonne Université, Université Paris Diderot, Paris, France
  • Iván Moyano

    University of Cambridge, UK
Uniqueness of the solution to the 2D Vlasov–Navier–Stokes system cover

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Abstract

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.

Cite this article

Daniel Han-Kwan, Évelyne Miot, Ayman Moussa, Iván Moyano, Uniqueness of the solution to the 2D Vlasov–Navier–Stokes system. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 37–60

DOI 10.4171/RMI/1120