Local Well-Posedness of Solutions to the MHD and Hall-MHD Systems

doi:10.13438/j.cnki.jdzk.2025.04.002

Abstract

Abstract: This paper studies the local well-posedness for the 3D generalized incompressible magneto-hydrodynamic (MHD) and Hall-magnetohydrodynamic (Hall-MHD) systems.Firstly,we present the estimations of the heat kernel in Morrey spaces.Then,by using Picard's fixed point argument,we prove that when parameters α₁,α₂ satisfy certain conditions and the initial data satisfies (u₀,b₀)∈Mr,p(R³)，where 1<r<p<+∞ and p>3，the solutions to these two systems are locally well-posed in homogeneous Morrey spaces.

Key words: MHD system, Hall-MHD system, local well-posedness, Morrey spaces

WANG Miaomiao, MA Deyi, BIE Qunyi. Local Well-Posedness of Solutions to the MHD and Hall-MHD Systems[J]. Journal of Jishou University(Natural Sciences Edition), 2025, 46(4): 5-10.

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