Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system

Dandan Ma; Fan Wu

doi:10.5802/crmath.379

Partial differential equations

Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system

Dandan Ma ¹; Fan Wu ¹

¹ College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 91-96.

Abstract

This paper concerns the energy conservation for the weak solutions to the Navier–Stokes–Maxwell system. Although the Maxwell equation with hyperbolic nature, we still establish a $L^{q} L^{p}$ type condition guarantee validity of the energy equality for the weak solutions. We mention that there no regularity assumption on the electric field $E$ .

Received: 2022-01-24
Accepted: 2022-06-09
Published online: 2023-01-12

DOI: 10.5802/crmath.379

Classification: 76W05, 35Q30, 35Q61

Author's affiliations:

Dandan Ma ¹; Fan Wu ¹

¹ College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Dandan Ma and Fan Wu},
     title = {Shinbrot{\textquoteright}s energy conservation criterion for the {3D} {Navier{\textendash}Stokes{\textendash}Maxwell} system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {91--96},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.379},
     language = {en},
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Dandan Ma; Fan Wu. Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 91-96. doi : 10.5802/crmath.379. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.379/

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