Global strong solution for the two‐dimensional magnetohydrodynamics equations with shearing‐periodic boundary conditions

Shintaro Kondo and Tatsuki Nakamura

Mathematische Nachrichten, 2025, vol. 298, issue 8, 2712-2739

Abstract: In this paper, we investigate the two‐dimensional (2D), two‐field magnetohydrodynamics (MHD) equations in the presence of a shear flow, assuming positive plasma viscosity and resistivity. We establish the global‐in‐time existence and uniqueness of a strong solution for the 2D two‐field MHD equations under shearing‐periodic boundary conditions, as proposed by Hawley et al. Moreover, we establish the existence and uniqueness of a strong solution for the linear advection‐diffusion equation under shearing‐periodic boundary condition by employing uniformly local L2$L^2$ spaces.

Date: 2025
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