The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria
Moussa, Ayman; Glass, Olivier; Han-Kwan, Daniel (2018), The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria, Archive for Rational Mechanics and Analysis, 230, 2. 10.1007/s00205-018-1253-1
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1612.06808
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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.
Subjects / KeywordsSpray model; incompressible Navier-Stokes equation; kinetic/ fluid coupling, stability
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