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Existence of strong solutions to the steady Navier-Stokes equations for a compressible heat-conductive fluid with large forces. (English. French summary) Zbl 1316.35226

Summary: We prove that there exists a strong solution to the Dirichlet boundary value problem for the steady Navier-Stokes equations of a compressible heat-conductive fluid with large external forces in a bounded domain \(\varOmega \subset \mathbb{R}^d\) (\(d = 2, 3\)), 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 proof is to split the equations into two parts, one of which is similar to the steady incompressible Navier-Stokes equations with large forces, while another part corresponds to the steady compressible heat-conductive Navier-Stokes equations with small forces. The existence is then established by dealing with these two parts separately, establishing uniform in the Mach number a priori estimates and exploiting the known results on the steady incompressible Navier-Stokes equations.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35M33 Initial-boundary value problems for mixed-type systems of PDEs
35D35 Strong solutions to PDEs
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