Home > Proceedings > Adv. Stud. Pure Math. > Nonlinear Dynamics in Partial Differential Equations > Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations for any specific heat ratio $\gamma>1$
Translator Disclaimer
VOL. 64 | 2015 Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations for any specific heat ratio $\gamma>1$
Song Jiang

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

## Abstract

In this paper we present the recent existence results from [14], [15] on weak solutions to the the steady Navier–Stokes equations for three-dimensional compressible isentropic flows with large data for any specific heat ratio $\gamma \gt 1$. The existence is proved in the framework of the weak convergence method due to Lions [16] by establishing a new a priori potential estimate of both pressure and kinetic energy (in a Morrey space) and using a bootstrap argument. The results presented in the current paper extend the existence of weak solutions in [9] from $\gamma \gt 4/3$ to $\gamma \gt 1$.

## Information

Published: 1 January 2015
First available in Project Euclid: 30 October 2018

zbMATH: 1335.35182

Digital Object Identifier: 10.2969/aspm/06410101

Subjects:
Primary: 35M12, 35M32, 76N10, 76N15