Abstract
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.
Citation
Davide Catania. "Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets." Int. J. Differ. Equ. 2013 1 - 13, 2013. https://doi.org/10.1155/2013/595819