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

doi:10.1007/s10473-022-0609-7

Abstract

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.

Key words: magnetic Prandtl equation, Gevrey function space, global well-posedness, auxiliary functions, loss of derivative

CLC Number:

76W05

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.

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