TY - JOUR
T1 - The Vlasov–Navier–Stokes System in a 2D Pipe
T2 - Existence and Stability of Regular Equilibria
AU - Glass, Olivier
AU - Han-Kwan, Daniel
AU - Moussa, Ayman
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2018/11/1
Y1 - 2018/11/1
N2 - 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.
AB - 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.
U2 - 10.1007/s00205-018-1253-1
DO - 10.1007/s00205-018-1253-1
M3 - Article
AN - SCOPUS:85047121128
SN - 0003-9527
VL - 230
SP - 593
EP - 639
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -