Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets

Abstract EN

We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics.

The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics.

We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives.

This is a preliminary result to the study of linearized variable-coefficient current-vortex sheets, a first step to prove the existence of solutions to the nonlinear problem.