Initial value problem for the free boundary magnetohydrodynamics with\n zero magnetic boundary condition

2014/09/15 by Donghyun Lee, Lee, Donghyun
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1409.4392

openalex publication_date 2014/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show local existence and uniqueness of plasma(fluid)-vaccum free boundary\nproblem of magnetohydrodynamic flow in three-dimensional space with infinite\ndepth setting when magnetic field is zero on the free boundary. We use\nSobolev-Slobodetskii space which was used in usual free boundary problem in\n[3,5,6,7,8,9]. We also show that this solution can be extended as long as we\nwant for sufficiently small initial data. Using the result of this paper we\nwill get a unique solution of (kinematic inviscid) - (magnetic non diffusive)\nfree boundary magnetohydrodynamics problem via (kinematic viscosity) -\n(magnetic diffusivity) limit in [10].\n

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