Global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity


Fan Wu




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.