English

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