On the existence of solutions to the Navier-Stokes-Poisson equations of a two-dimensional compressible flow. (English) Zbl 1107.76065

Summary: We consider 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 \(p(\rho)=a\rho \log^{d}(\rho)\) for large \(\rho\). Here \(d>1\) and \(a>0\).


76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30 Navier-Stokes equations
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