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

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 E L4L4 and Vb E La L a. Moreover, as a corollary, we also obtain the energy conservation criterion for a Leray-Hopf weak solution.

Automated summary

This paper discusses the global energy conservation for distributional solutions to incompressible Hall-MHD equations without resistivity. Building upon the works of Tan and Wu in [arXiv:2111.13547v2] and Wu in [J. Math. Fluid Mech. 24,111 (2022)], the energy balance is established for a distributional solution in whole spaces Rd(d ≥ 2), given that u, b ∈ L4L4 and Vb ∈ LaLa. Furthermore, as a corollary, the energy conservation criterion for a Leray-Hopf weak solution is also obtained.