Weak solutions to the three-dimensional steady full compressible Navier–Stokes system. (November 2015)

• Record Type: Journal Article
• Authors: Zhong, Xin
• Is Part Of: Nonlinear analysis. Volume 127(2015)
• Page Start: 71
• Page End: 93
• Publication Date: 2015-11
• Subjects: 76N10 -- 35Q30; Steady fluids -- Full compressible Navier–Stokes system -- Weak solution; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.06.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: 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 ) ρ e ( ρ, θ ) the existence of weak solutions for any γ > 5 4 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.