Initial value problem for the free boundary magnetohydrodynamics with zero magnetic boundary condition
Analysis of PDEs
2017-10-09 v2
Abstract
We show local existence and uniqueness of plasma(fluid)-vaccum free boundary problem of magnetohydrodynamic flow in three-dimensional space with infinite depth setting when magnetic field is zero on the free boundary. We use Sobolev-Slobodetskii space which was used in usual free boundary problem in [3,5,6,7,8,9]. We also show that this solution can be extended as long as we want for sufficiently small initial data. Using the result of this paper we will get a unique solution of (kinematic inviscid) - (magnetic non diffusive) free boundary magnetohydrodynamics problem via (kinematic viscosity) - (magnetic diffusivity) limit in [10].
Cite
@article{arxiv.1409.4392,
title = {Initial value problem for the free boundary magnetohydrodynamics with zero magnetic boundary condition},
author = {Donghyun Lee},
journal= {arXiv preprint arXiv:1409.4392},
year = {2017}
}
Comments
Accepted in Comm. Math. Sci. (2017)