## Advanced Studies in Pure Mathematics

### Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations for any specific heat ratio $\gamma>1$

Song Jiang

#### 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 $\gamma \gt 1$.

#### Article information

Dates
First available in Project Euclid: 30 October 2018

Jiang, Song. Existence of weak solutions to the three-dimensional steady compressible Navier–Stokes equations for any specific heat ratio $\gamma&gt;1$. Nonlinear Dynamics in Partial Differential Equations, 101--111, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410101. https://projecteuclid.org/euclid.aspm/1540934206