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

Abstract

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.