International Journal of Differential Equations
Volume 2013 (2013), Article ID 595819, 13 pages
Research Article

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

Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy

Received 29 May 2012; Revised 21 December 2012; Accepted 27 December 2012

Academic Editor: Helge Holden

Copyright © 2013 Davide Catania. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.