Open AccessLarge-time behaviors of the solution to 3D compressible Navier-Stokes equations in half space with Navier boundary conditions
Author(s) -
Teng Wang,
Yi Wang
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021080
Subject(s) - mathematics , boundary value problem , mathematical analysis , compressibility , boundary (topology) , space (punctuation) , isentropic process , physics , mechanics , linguistics , philosophy
We are concerned with the large-time asymptotic behaviors towards the planar rarefaction wave to the three-dimensional (3D) compressible and isentropic Navier-Stokes equations in half space with Navier boundary conditions. It is proved that the planar rarefaction wave is time-asymptotically stable for the 3D initial-boundary value problem of the compressible Navier-Stokes equations in \begin{document}$ \mathbb{R}^+\times \mathbb{T}^2 $\end{document} with arbitrarily large wave strength. Compared with the previous work [ 17 , 16 ] for the whole space problem, Navier boundary conditions, which state that the impermeable wall condition holds for the normal velocity and the fluid tangential velocity is proportional to the tangential component of the viscous stress tensor on the boundary, are crucially used for the stability analysis of the 3D initial-boundary value problem.