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Research Article | Open Access

Energy equality for the compressible Navier-Stokes-Korteweg equations

Hui Fang1, Yihan Fan1,2, Yanping Zhou1,2( )
College of Science, China Three Gorges University, Yichang 443002, China
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China
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Abstract

In this paper, we investigate the problem of energy equality of the two and three dimensional compressible Navier-Stokes-Korteweg equations with general pressure law. By using the commutator estimation to deal with the nonlinear terms, we obtain the sufficient conditions for the regularity of weak solutions to conserve the energy.

Keywords

Navier-Stokes-Korteweg equationscompressible fluidsenergy equality
CLC number: 35Q35, 76N10

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5808-5820
DOI: 10.3934/math.2022321

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Cite this article:
Fang H, Fan Y, Zhou Y. Energy equality for the compressible Navier-Stokes-Korteweg equations. AIMS Mathematics, 2022, 7(4): 5808-5820. https://doi.org/10.3934/math.2022321

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Received: 28 October 2021
Revised: 22 December 2021
Accepted: 05 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)