Quantitative regularity for the MHD equations via the localization technique in frequency space
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912123175567360 |
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| author | Lai, Baishun Zhang, Shihao |
| author_facet | Lai, Baishun Zhang, Shihao |
| contents | In this paper, we employ the localization technique in frequency space developed by Tao in \cite{MR4337421} to investigate the quantitative estimates for the MHD equations. With the help of quantitative Carleman inequalities given by Tao in \cite{MR4337421} and the pigeonhole principle, we establish the quantitative regularity for the critical $L^3$ norm bounded solutions which enables us explicitly quantify the blow-up behavior in terms of $L^3$ norm near a potential first-time singularity. Some technical innovations, such as introducing the corrector function, are required due to the fact that the scales are inconsistent between the magnetic field and the vorticity field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11419 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative regularity for the MHD equations via the localization technique in frequency space Lai, Baishun Zhang, Shihao Analysis of PDEs In this paper, we employ the localization technique in frequency space developed by Tao in \cite{MR4337421} to investigate the quantitative estimates for the MHD equations. With the help of quantitative Carleman inequalities given by Tao in \cite{MR4337421} and the pigeonhole principle, we establish the quantitative regularity for the critical $L^3$ norm bounded solutions which enables us explicitly quantify the blow-up behavior in terms of $L^3$ norm near a potential first-time singularity. Some technical innovations, such as introducing the corrector function, are required due to the fact that the scales are inconsistent between the magnetic field and the vorticity field. |
| title | Quantitative regularity for the MHD equations via the localization technique in frequency space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.11419 |