Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations (Q805435)

Considering the slightly compressible Navier-Stokes equations \[ (1)\quad u_ t+(u\nabla)u+\nabla p=\nu \Delta u+F, \] \[ \epsilon^ 2\{p_ t+(u\nabla)p\}+\nabla u=g, \] the authors discuss the Cauchy problem for the 1-periodic in x and y solutions of the limiting equations for the equations (1) and the initial-boundary value problem with prescribed inflow velocity at \(x=0\) and outflow velocity at \(x=1\). The idea is to approximate the solutions of the compressible N-S equations by the sum of the solutions of the incompressible equations plus a function which is highly oscillatory in time. It is shown that the oscillatory term can be described by the wave equations. Besides the validity of the bounded derivative principle for this situation is established.