Low Mach number limit for the compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition

Boundary value problems

Yunting Ding¹  Dandan Ren¹  Xinfeng Liang¹ 

[1] School of Mathematics and Big Data, Anhui University of Science and Technology, Taifeng Street, 232001, Huainan, P.R. China;

关键词: Navier–Stokes equations;    Density-dependent viscosity;    Bounded domain;    Low Mach number limit;    Global existence;   

DOI  :  10.1186/s13661-020-01455-9

来源: Springer

【 摘 要 】

In this paper, we consider the three-dimensional compressible Navier–Stokes equations with density-dependent viscosity and vorticity-slip boundary condition in a bounded smooth domain. The main idea is to derive the uniform estimates for both time and the Mach number. The difficulty is dealing with density-dependent viscosity terms carefully. With the uniform estimates, we can verify the low Mach limit of the global strong solutions of compressible Navier–Stokes equations and the global existence and uniqueness of the strong solution of incompressible Navier–Stokes equations around a steady state.

【 授权许可】

CC BY