Weak solutions to the three-dimensional steady full compressible Navier–Stokes system

We study the motion of the steady compressible viscous heat-conductive fluid in a bounded three dimensional domain governed by the full Navier–Stokes system. For the pressure law of the form p(ρ,θ)=(γ−1)ρe(ρ,θ)p(ρ,θ)=(γ−1)ρe(ρ,θ) the existence of weak solutions for any γ>54 is obtained. Our method relies upon the weighted estimates of both pressure and kinetic energy for the approximate system. Other tools such as effective viscous flux and oscillation defect measure developed by Lions and Feireisl respectively are also needed.