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Regularity criterion on the energy conservation for the compressible Navier–Stokes equations

Part of: Equations of mathematical physics and other areas of application Incompressible inviscid fluids Compressible fluids and gas dynamics, general

Published online by Cambridge University Press:  11 December 2020

Zhilei Liang Open the ORCID record for Zhilei Liang [Opens in a new window]
Zhilei Liang*
Affiliation:
School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China (zhilei0592@gmail.com)
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Abstract

This paper concerns the energy conservation for the weak solutions of the compressible Navier–Stokes equations. Assume that the density is positively bounded, we work on the regularity assumption on the gradient of the velocity, and establish a Lp–Ls type condition for the energy equality to hold in the distributional sense in time. We mention that no regularity assumption on the density derivative is needed any more.

Keywords

Compressible Navier–Stokesenergy conservationweak solutions

MSC classification

Primary: 35Q30: Navier-Stokes equations
Secondary: 76B03: Existence, uniqueness, and regularity theory 76N10: Existence, uniqueness, and regularity theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1954 - 1971
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Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press.

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