Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
Analysis of PDEs
2022-11-03 v4
Abstract
We show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the Rayleigh-Taylor sign condition holds true initially. This result is a continuation of the authors' previous works [17,32,16]. Our proof is based on the combination of the techniques developed in our previous works [17,32,16], Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.
Keywords
Cite
@article{arxiv.2109.05400,
title = {Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics},
author = {Xumin Gu and Chenyun Luo and Junyan Zhang},
journal= {arXiv preprint arXiv:2109.05400},
year = {2022}
}
Comments
35 pages. Final version, accepted by Nonlinearity. We extend the result to the case of a general diffeomorphism