Shanshan Yang, Bin Han, Hong-Kun Xu, Existence of global axisymmetric solutions for a 3D inhomogeneous incompressible hall-magnetohydrodynamic system

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DOI: 10.23952/jnva.10.2026.1.02

Volume 10, Issue 1, 1 April 2026, Pages 41-59

Abstract. We study the global well-posedness of an inhomogeneous incompressible Hall-MHD system in the whole space ${\Bbb R}^3$ . Let $\rho_0$ be the initial density of the fluids. Under certain appropriate smallness assumptions on ${a_0}/{r}$ , where $a_0=({1}/{\rho_0})-1$ and $r=(x_1^2+x_2^2)^{1/2}$ , we demonstrate the global regularity of the solutions to the Cauchy problem of the inhomogeneous Hall-MHD system with axisymmetric initial data, where the swirl component of the velocity field and magnetic vorticity field vanish.

How to Cite this Article:
S. Yang, B. Han, H.K. Xu, Existence of global axisymmetric solutions for a 3D inhomogeneous incompressible hall-magnetohydrodynamic system, J. Nonlinear Var. Anal. 10 (2026), 41-59.