On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow

In this paper, we consider the Navier-Stokes-Poisson equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying p(rhov)=arhovlogd (rhov) for large rhov. Here d>1 and a>0.