Abstract
We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer. A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2. The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.
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Dedicated to Professor Banghe LI on the occasion of his 80th birthday
W.-X. Li’s research was supported by NSF of China (11871054, 11961160716, 12131017) and the Natural Science Foundation of Hubei Province (2019CFA007). T. Yang’s research was supported by the General Research Fund of Hong Kong CityU (11304419).
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Li, WX., Xu, R. & Yang, T. Global well-posedness of a Prandtl model from MHD in Gevrey function spaces. Acta Math Sci 42, 2343–2366 (2022). https://doi.org/10.1007/s10473-022-0609-7
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DOI: https://doi.org/10.1007/s10473-022-0609-7
Key words
- magnetic Prandtl equation
- Gevrey function space
- global well-posedness
- auxiliary functions
- loss of derivative