Incompressible limit of strong solutions to 3-D Navier-Stokes equations with Navier's slip boundary condition for all time

Abstract

This paper studies the incompressible limit of global strong solutions to the three-dimensional compressible Navier-Stokes equations associated with Navier's slip boundary condition, provided that the time derivatives, up to first order, of solutions are bounded initially. The main idea is to derive a differential inequality with decay, so that the estimates are bounded uniformly both in the Mach number 0<\epsilon<=\epsilon 0 for some \epsilon 0>0 and the time t>=0.