On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914049945501696 |
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| author | Zhang, Junyan |
| author_facet | Zhang, Junyan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_00421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension Zhang, Junyan Analysis of PDEs 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. |
| title | On the Incompressible Limit of Current-Vortex Sheets with or without Surface Tension |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.00421 |