INITIAL VALUE PROBLEM FOR THE FREE-BOUNDARY MAGNETOHYDRODYNAMICS WITH ZERO MAGNETIC BOUNDARY CONDITION
SCIE
SCOPUS
- Title
- INITIAL VALUE PROBLEM FOR THE FREE-BOUNDARY MAGNETOHYDRODYNAMICS WITH ZERO MAGNETIC BOUNDARY CONDITION
- Authors
- LEE, DONGHYUN
- Date Issued
- 2018-08
- Publisher
- INT PRESS BOSTON
- Abstract
- We show local well-posedness of fluid-vacuum free-boundary magnetohydrodynamic (MHD) with both kinematic viscosity and magnetic diffusivity under the gravity force. We consider three-dimensional problem with finite depth and impose zero magnetic field condition on the free boundary and in vacuum. Sobolev-Slobodetskii space (fractional Sobolev space) is used to perform energy estimates. Main difficulty is to control strong nonlinear couplings between velocity and magnetic fields. In [D. Lee, SIAM J. Math. Anal., 49(4):2710-2789, 2017], we send both kinematic viscosity and magnetic diffusivity to zero with same speed to get ideal (inviscid) free-boundary magnetohydrodynamics using the result of this paper.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/94512
- DOI
- 10.4310/CMS.2018.v16.n3.a1
- ISSN
- 1539-6746
- Article Type
- Article
- Citation
- Communications in Mathematical Sciences, vol. 16, no. 3, page. 589 - 615, 2018-08
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