Articles

GLOBAL WELL-POSEDNESS OF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES

  • Weixi LI ,
  • Rui XU ,
  • Tong YANG
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  • 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
    2. Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China;
    3. Department of Mathematics, City University of Hong Kong, Hong Kong, China

Received date: 2022-07-07

  Online published: 2022-12-16

Supported by

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).

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.

Cite this article

Weixi LI , Rui XU , Tong YANG . GLOBAL WELL-POSEDNESS OF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES[J]. Acta mathematica scientia, Series B, 2022 , 42(6) : 2343 -2366 . DOI: 10.1007/s10473-022-0609-7

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