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

Abstract

Abstract 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.

Keywords

• Navier–Stokes equations
• Density-dependent viscosity
• Bounded domain
• Low Mach number limit
• Global existence