Steady compressible Navier-Stokes-Fourier equations with Dirichlet boundary condition for the temperature (Q6614874)

The author studies the existence of large solutions to the steady compressible Navier-Stokes-Fourier equations with Dirichlet boundary condition for the temperature. Based on the recent result from [\textit{N. Chaudhuri} and \textit{E. Feireisl}, Appl. Anal. 101, No. 12, 4076--4094 (2022; Zbl 1496.35277)] for the evolutionary compressible Navier-Stokes-Fourier equations, and under some (growth) conditions upon the pressure, viscosity and heat-conductivity, the author proves the existence of a variational entropy/weak ballistic solution 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 the author to obtain estimates of the temperature by exploiting the growth conditions.\N\NFor the entire collection see [Zbl 1515.76005].