Nonlinear stability of current-vortex sheet to the incompressible MHD equations

Abstract

In this paper, we solve a long-standing open problem: nonlinear stability of current-vortex sheet in the ideal incompressible Magneto-Hydrodynamics under the linear stability condition. This result gives a first rigorous confirmation of the stabilizing effect of the magnetic field on Kelvin-Helmholtz instability.

44 pages

References in corpus (2)

• A priori estimates for 3D incompressible current-vortex sheets
• Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains

Cited by in corpus (1)

• On the motion of free interface in two-dimensional ideal incompressible MHD