Incompressible limit and stability of all-time solutions to 3-D full Navier-Stokes equations for perfect gases

Abstract

This paper studies the incompressible limit and stability of global strong solutions to the three-dimensional full compressible Navier-Stokes equations, where the initial data satisfy the “well-prepared” conditions and the velocity field and temperature enjoy the slip boundary condition and convective boundary condition, respectively. The uniform estimates with respect to both the Mach number \(\varepsilon \in \left( {0,\overline \varepsilon } \right]'\) and time t ∈ [0,∞) are established by deriving a differential inequality with decay property, where \(\overline \varepsilon \in \left( {0,1} \right]\) is a constant. As the Mach number vanishes, the global solution to full compressible Navier-Stokes equations converges to the one of isentropic incompressible Navier-Stokes equations in t ∈ [0,+∞). Moreover, we prove the exponentially asymptotic stability for the global solutions of both the compressible system and its limiting incompressible system.