Filomat 2023 Volume 37, Issue 28, Pages: 9741-9751
https://doi.org/10.2298/FIL2328741W
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Global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity
Wu Fan (College of Science, Nanchang Institute of Technology, Nanchang, Jiangxi, China), wufan0319@yeah.net
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] and Wu 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.
Keywords: Energy conservation, Non-resistive Hall-MHD system, Distributional solutions, Leray-Hopf weak solution
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