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WEAK SOLUTIONS TO EQUATIONS OF STEADY COMPRESSIBLE HEAT CONDUCTING FLUIDS

PIOTR B. MUCHA

Institute of Applied Mathematics and Mechanics, University of Warsaw, ul. Banacha 2, Warszawa 02-097, Poland

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and

MILAN POKORNÝ

Mathematical Institute of Charles University, Sokolovská 83, Praha 186 75, Czech Republic

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https://doi.org/10.1142/S0218202510004441Cited by:28 (Source: Crossref)

Abstract

We consider the steady compressible Navier–Stokes–Fourier system in a bounded three-dimensional domain. We prove the existence of a solution for arbitrarily large data under the assumption that the pressure p(ϱ, θ) ~ ϱθ + ϱ^γ for assuming either the slip or no-slip boundary condition for the velocity and the Newton boundary condition for the temperature. The regularity of solutions is determined by the basic energy estimates, constructed for the system.

Keywords:

AMSC: 35Q30, 76N10

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