Incompressible limit of global strong solutions to 3-D barotropic Navier–Stokes equations with well-prepared initial data and Navier's slip boundary conditions

Abstract

This paper studies the incompressible limit of global strong solutions to the three-dimensional barotropic Navier–Stokes equations associated with Navier's slip boundary conditions, provided that the initial data are sufficiently small, and “well-prepared” in the sense 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 ϵ∈(0,ϵ0] (for some ϵ0>0) and the time t∈[0,+∞).