Well-posedness of the free boundary problem in incompressible MHD with surface tension

TL;DR

This paper proves the local well-posedness of a two-phase incompressible MHD flow with surface tension and shows solutions converge to the no-surface-tension case as surface tension vanishes.

Contribution

It establishes the well-posedness of the free boundary problem in incompressible MHD with surface tension and analyzes the zero surface tension limit.

Findings

Proved local well-posedness of the problem.

Demonstrated convergence as surface tension tends to zero.

Characterized the behavior of solutions without surface tension.

Abstract

In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. We first prove the local well-posedness of the two phase flow problem with surface tension, then demonstrate that as surface tension tends to zero, the solution of the two phase flow problem with surface tension converges to the solution of the two phase flow problem without surface tension.