On convergence to equilibria of flows of compressible viscous fluids under in/out–flux boundary conditions

Jan Březina; Eduard Feireisl; Antonín Novotný

doi:10.3934/dcds.2021009

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2021, Volume 41, Issue 8: 3615-3627. Doi: 10.3934/dcds.2021009

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On convergence to equilibria of flows of compressible viscous fluids under in/out–flux boundary conditions

1.
Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan
2.
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Praha 1, Czech Republic, Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
3.
IMATH, EA 2134, Université de Toulon, BP 20132, 83957 La Garde, France

^* Corresponding author: Jan Březina
^* Corresponding author: Jan Březina

Received: May 2020

Revised: October 2020

Early access: January 2021

Published: August 2021

Jan Březina and Eduard Feireisl, The work of E.F. was partially supported by the Czech Sciences Foundation (GAČR), Grant Agreement 18-05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.
Antonín Novotný, The work of A.N. was supported by Brain Pool program funded by the Ministry of Science and ICT through the National Research Foundation of Korea (NRF-2019H1D3A2A01101128)..

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Abstract

We consider the barotropic Navier–Stokes system describing the motion of a compressible Newtonian fluid in a bounded domain with in and out flux boundary conditions. We show that if the boundary velocity coincides with that of a rigid motion, all solutions converge to an equilibrium state for large times.

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Mathematics Subject Classification: 35Q30, 37L15, 76N15.

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References

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