TY - JOUR
T1 - Global Well-Posedness of a Prandtl Model from MHD in Gevrey Function Spaces
AU - Li, Weixi
AU - Xu, Rui
AU - Yang, Tong
PY - 2022/11
Y1 - 2022/11
N2 - 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.
AB - 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.
KW - 35M33
KW - 35Q35
KW - 76W05
KW - auxiliary functions
KW - Gevrey function space
KW - global well-posedness
KW - loss of derivative
KW - magnetic Prandtl equation
UR - http://www.scopus.com/inward/record.url?scp=85137522515&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85137522515&origin=recordpage
U2 - 10.1007/s10473-022-0609-7
DO - 10.1007/s10473-022-0609-7
M3 - 21_Publication in refereed journal
VL - 42
SP - 2343
EP - 2366
JO - Acta Mathematica Scientia
JF - Acta Mathematica Scientia
SN - 0252-9602
IS - 6
ER -