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The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria. (English) Zbl 1398.35242
Summary: 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.

MSC:
35Q83 Vlasov equations
35Q30 Navier-Stokes equations
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
76D05 Navier-Stokes equations for incompressible viscous fluids
35B65 Smoothness and regularity of solutions to PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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