Analytic current-vortex sheets in incompressible magnetohydrodynamics

TL;DR

This paper proves local-in-time existence and uniqueness of solutions for analytic initial data in the problem of current-vortex sheets in ideal incompressible magnetohydrodynamics, using a Cauchy-Kowalevskaya theorem.

Contribution

It provides a rigorous mathematical proof of local well-posedness for analytic initial conditions in MHD current-vortex sheets, a problem previously lacking such results.

Findings

Existence of solutions established for analytic initial data.

Uniqueness of solutions proved within the same class.

Application of Cauchy-Kowalevskaya theorem to MHD problem.

Abstract

In this paper, we address the problem of current-vortex sheets in ideal incompressible magnetohydrodynamics. More precisely, we prove a local-in-time existence and uniqueness result for analytic initial data using a Cauchy-Kowalevskaya theorem.