Comptes Rendus
Equations aux dérivées partielles
Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system
Dandan Ma1 ; Fan Wu1 
1 College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 91-96.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.379
Classification : 76W05, 35Q30, 35Q61
Dandan Ma 1 ; Fan Wu 1

1 College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi 330099, China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2023__361_G1_91_0,
     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},
}
TY  - JOUR
AU  - Dandan Ma
AU  - Fan Wu
TI  - Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system
JO  - Comptes Rendus. Mathématique
PY  - 2023
SP  - 91
EP  - 96
VL  - 361
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.379
LA  - en
ID  - CRMATH_2023__361_G1_91_0
ER  - 
%0 Journal Article
%A Dandan Ma
%A Fan Wu
%T Shinbrot’s energy conservation criterion for the 3D Navier–Stokes–Maxwell system
%J Comptes Rendus. Mathématique
%D 2023
%P 91-96
%V 361
%I Académie des sciences, Paris
%R 10.5802/crmath.379
%G en
%F CRMATH_2023__361_G1_91_0
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/

[1] Diogo Arsénio; Gallagher Isabelle Solutions of Navier-Stokes-Maxwell systems in large energy spaces, Trans. Am. Math. Soc., Volume 373 (2020) no. 6, pp. 3853-3884 | DOI | MR | Zbl

[2] Renjun Duan Green’s function and large time behavior of the Navier-Stokes-Maxwell system, Anal. Appl., Singap., Volume 10 (2012) no. 2, pp. 133-197 | DOI | MR | Zbl

[3] Eberhard Hopf Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., Volume 4 (1951) no. 1-6, pp. 213-231 | Zbl

[4] Ol’ga A. Ladyzhenskaya; Vsevolod A. Solonnikov; Nina N. Ural’tseva Linear and quasi-linear equations of parabolic type, Translations of Mathematical Monographs, 23, American Mathematical Society, 1968 | Zbl

[5] Jean Leray Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math., Volume 63 (1934) no. 1, pp. 193-248 | DOI | MR | Zbl

[6] Jacques-Louis Lions Sur la régularité et l’unicité des solutions turbulentes des équations de Navier-Stokes, Rend. Semin. Mat., Torino, Volume 30 (1960), pp. 16-23 | Zbl

[7] Pierre-Louis Lions Mathematical Topics in Fluid Mechanics, Vol. 1: Incompressible Models., Oxford Lecture Series in Mathematics and its Applications, 3, Oxford University Press, 1996 | Zbl

[8] Nader Masmoudi Global well posedness for the Maxwell-Navier-Stokes system in 2D, J. Math. Pures Appl., Volume 93 (2010) no. 6, pp. 559-571 | DOI | MR | Zbl

[9] Marvin Shinbrot The energy equation for the Navier-Stokes system, SIAM J. Math. Anal., Volume 5 (1975) no. 6, pp. 948-954 | DOI | MR | Zbl

[10] Ibrahim Slim; Keraani Sahbi Global small solutions for the Navier-Stokes-Maxwell system, SIAM J. Math. Anal., Volume 43 (2011) no. 5, pp. 2275-2295 | DOI | MR | Zbl

[11] Wenke Tan; Fan Wu On the energy equality for the 3D incompressible viscoelastic flows (2021) (https://arxiv.org/abs/2111.13547v1)

[12] Wenke Tan; Z. Yin The energy conservation and regularity for the Navier-Stokes equations (2021) (https://arxiv.org/abs/2107.04157)

[13] Cheng Yu A new proof to the energy conservation for the Navier-Stokes equations (2016) (https://arxiv.org/abs/1604.05697)

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Uniqueness theorem for a coupled system of wave equations with incomplete internal observation and application to approximate controllability

Tatsien Li; Bopeng Rao

C. R. Math (2022)

Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports

Karine Beauchard; Michela Egidi; Karel Pravda-Starov

C. R. Math (2020)

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations

Clément Cancès; Juliette Venel

C. R. Math (2023)