On the Stokes approximation equations for two-dimensional compressible flows

Abstract

We deal with the unique global strong solution orclassical solution to the Cauchy problem of the 2D Stokesapproximation equations for the compressible flows with the densitybeing some positive constant on the far field for arbitrarily largeinitial data, which may contain vacuum states. First, we prove thatthe density is bounded from above independently of time. Secondly,we show that if the initial density contains vacuum at least at onepoint, then the global strong (or classical) solution must blow upas time goes to infinity.