Steady Compressible Navier-Stokes-Fourier Equations with Dirichlet Boundary Condition for the Temperature
2022
Abstract
Based on the recent result from Chaudhuri and Feireisl (Navier-Stokes-Fourier system with Dirichlet boundary conditions, 2021. arXiv:2106.05315) for the evolutionary compressible Navier-Stokes-Fourier equations we present the proof of existence of a weak solution for the steady system with Dirichlet boundary condition for the temperature without any restriction on the size of the data. The weak formulation of the equations for the temperature is based on the total energy balance and entropy inequality with compactly supported test functions and a steady version of the ballistic energy inequality which allows to obtain estimates of the temperature.