2024/10/28 by Yuan Cai, Zhen Lei, Cai, Yuan +1
Physics and Astronomy · Earth and Planetary Sciences · #Solar and Space Plasma Dynamics #Ionosphere and magnetosphere dynamics #Geophysics and Gravity Measurements
paper · pdf · doi:10.48550/arxiv.2410.20782
The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal incompressible magnetohydrodynamics under the strong horizontal background magnetic field. This appears to be the first result on the global solutions of the free boundary problems for the ideal (inviscid and non-resistive) incompressible rotational fluids. The strong magnetic field plays a crucial role in the global in time stabilization effect. The proof relies on the understanding of the interplay between the dynamics of the fluids inside the domain and on the free interface, a design of multiple-level energy estimates with different weights, and the inherent structures of the problem.