Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets. (6th March 2013)

• Record Type: Journal Article
• Authors: Catania, Davide
• Other Names: Holden Helge Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2013(2013)
• Publication Date: 2013-03-06
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2013/595819
• Languages: English
• ISSNs: 1687-9643

Abstract

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.