Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations-Reference-Cited by-同舟云学术

Some results on free boundary problems of incompressible ideal magnetohydrodynamics equations

Published:2022 Issue:2 Volume:30 Page:404-424
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Hao Chengchun, ,Luo Tao, ,

Abstract

<abstract>We survey some recent results related to free boundary problems of incompressible ideal magnetohydrodynamics equations, and present the main ideas in the proofs of the ill-posedness in 2D when the Taylor sign condition is violated given [<xref ref-type="bibr" rid="b1">1</xref>], and the well-posedness of a linearized problem given in [<xref ref-type="bibr" rid="b2">2</xref>] in general $ n $-dimensions ($ n \geqslant 2 $) when the Taylor sign condition is satisfied and the free boundaries are closed.</abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference45 articles.

1. C. Hao, T. Luo, Ill-posedness of free boundary problem of the incompressible ideal MHD, Commun. Math. Phys., 376 (2020), 259–286. https://doi.org/10.1007/s00220-019-03614-1

2. C. Hao, T. Luo, Well-posedness for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations, J. Differential Equations, 299 (2021), 542–601. https://doi.org/10.1016/j.jde.2021.07.030

3. C. Hao, T. Luo, A priori estimates for free boundary problem of incompressible inviscid magnetohydrodynamic flows, Arch. Ration. Mech. Anal., 212 (2014), 805–847. https://doi.org/10.1007/s00205-013-0718-5

4. S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in $2$-D, Invent. Math., 130 (1997), 39–72. https://doi.org/10.1007/s002220050177

5. S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc., 12 (1999), 445–495. https://doi.org/10.1090/S0894-0347-99-00290-8