Incompressible limit of the non-isentropic Navier–Stokes equations with well-prepared initial data in three-dimensional bounded domains

Abstract

This paper studies the incompressible limit of the non-isentropic Navier–Stokes equations for viscous polytropic flows with zero thermal coefficient in three-dimensional bounded C 4 -domains. The uniform estimates in the Mach number, which exclude the estimate of high-order derivatives of the velocity in the normal directions to the boundary, are established within a short time interval independent of Mach number ϵ ∈ ( 0 , 1 ] , provided that the initial data are well-prepared.