On the Steady Solutions to a Model of Compressible Heat Conducting Fluid in Two Space Dimensions

Abstract

We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(\varrho,ϑ)∼\varrhoϑ+\varrho ln^α(1+\varrho). For the heat flux q∼-(1+ϑ^m)∇ϑ we show the existence of a weak solution provided α > max{1,1/m}, m > 0. This improves the recent result from [1].