The Vlasov–Navier–Stokes System in a 2D Pipe: Existence and Stability of Regular Equilibria

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Abstract

In this paper, we study the Vlasov–Navier–Stokes system in a 2D pipe with partially absorbing boundary conditions. We show the existence of stationary states for this system near small Poiseuille flows for the fluid phase, for which the kinetic phase is not trivial. We prove the asymptotic stability of these states with respect to appropriately compactly supported perturbations. The analysis relies on geometric control conditions which help to avoid any concentration phenomenon for the kinetic phase.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CEREMADE, Université Paris-Dauphine, CNRS UMR 7534, PSL Research UniversityParis Cedex 16France
  2. 2.CMLS - École polytechnique, CNRSPalaiseau CedexFrance
  3. 3.Sorbonne Université, CNRS, UMR 7598, LJLLParisFrance

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