On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension
Abstract
This is the second part of the two-paper sequence, which aims to present a comprehensive study for current-vortex sheets in ideal compressible magnetohydrodynamics (MHD). The local well-posedness of current-vortex sheets with surface tension has been proved in the first part of the paper sequence [63]. In this paper, we prove the incompressible and zero-surface-tension limits under certain stability conditions. The proof of uniform estimates relies on the analysis of the evolution equation of the free interface via a paradifferential approach, the wave equation of the pressure and a weighted anisotropic structure in vorticity analysis.
Keywords
Cite
@article{arxiv.2405.00421,
title = {On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension},
author = {Junyan Zhang},
journal= {arXiv preprint arXiv:2405.00421},
year = {2025}
}
Comments
45 pages. v2-v3: some typos corrected. v1:The preprint arXiv:2312.11254v2(110 pages) will be split into two papers for submission due to the length issue, and this is the second part. arXiv admin note: text overlap with arXiv:2312.11254