Geodesic
Global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity
Filomat, Tome 37 (2023) no. 28, p. 9741

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DOI

This paper concerns the global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity. Motivated by the works of Tan and Wu in [arXiv:2111.13547v2] andWu in [J. Math. Fluid Mech. 24, 111 (2022)], we establish the energy balance for a distributional solution in whole spaces Rd(d ≥ 2) provided that u, b ∈ L4L4 and ∇b ∈ L8 3 L8 3 . Moreover, as a corollary, we also obtain the energy conservation criterion for a Leray-Hopf weak solution.
DOI : 10.2298/FIL2328741W
Classification : 76W05 35Q35
Keywords: Energy conservation, Non-resistive Hall-MHD system, Distributional solutions, Leray-Hopf weak solution 
Fan Wu. Global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity. Filomat, Tome 37 (2023) no. 28, p. 9741 . doi: 10.2298/FIL2328741W
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     author = {Fan Wu},
     title = {Global energy conservation for distributional solutions to incompressible {Hall-MHD} equations without resistivity},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2328741W},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2328741W/}
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