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

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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

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 101-111

Dates
Received: 3 April 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934206

Digital Object Identifier
doi:10.2969/aspm/06410101

Zentralblatt MATH identifier
1335.35182

Subjects
Primary: 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30] 35M12: Boundary value problems for equations of mixed type 35M32: Boundary value problems for systems of mixed type 76N15: Gas dynamics, general

Keywords
Steady compressible Navier–Stokes equations existence for $\gamma \gt 1$ potential estimate effective viscous flux

Citation

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


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