Long time existence of the slightly compressible Navier-Stokes equations in bounded domains

We are concerned with the long time existence of strong solutions to the initial boundary value problem with slip boundary conditions for the compressible Navier-Stokes equations in three-dimensional simply connected bounded domains. We verify that the barotropic Navier-Stokes equations admit a unique strong solution on the time interval where the solution to the incompressible Navier-Stokes equations exists and is reasonably smooth, when the Mach number is sufficiently small. Furthermore, we obtain the uniform convergence of strong solutions for the compressible system toward those for the corresponding incompressible system on that time interval.