On the existence of solutions to the Navier–Stokes equations of a two‐dimensional compressible flow

We consider the Navier–Stokes 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(?) = a?log^d(?) for large ?. Here d>1 and a > 0. Copyright © 2003 John Wiley & Sons, Ltd.