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

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  • Davide Catania

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.

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  • Davide Catania, 2013. "Existence and Stability for the 3D Linearized Constant-Coefficient Incompressible Current-Vortex Sheets," International Journal of Differential Equations, Hindawi, vol. 2013, pages 1-13, March.
    • Handle: RePEc:hin:jnijde:595819
    DOI: 10.1155/2013/595819
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