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We prove that there exists a strong solution to the Dirichlet boundary valueproblem for the steady Navier-Stokes equations of a compressibleheat-conductive fluid with large external forces in a bounded domain $R^d (d =2, 3)$, provided that the Mach number is appropriately small. At the same time,the low Mach number limit is rigorously verified. The basic idea in the proofis to split the equations into two parts, one of which is similar to the steadyincompressible Navier-Stokes equations with large forces, while another partcorresponds to the steady compressible heat-conductive Navier-Stokes equationswith small forces. The existence is then established by dealing with these twoparts separately, establishing uniform in the Mach number a priori estimatesand exploiting the known results on the steady incompressible Navier-Stokesequations.

Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces