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

This paper studies the incompressible limit of global strong solutions to the threedimensional 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 ǫ ∈ (0,ǫ0] (for some ǫ0 > 0) and the time t ∈ [0,+∞).