Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regine
Abstract
In this paper, we prove local existence and uniqueness for the 2D Prandtl-Hartmann regine in weighted Sobolev spaces. Our proof is based on using uniform estimates of the regularized parabolic equation and maximal principle under the Oleinik's monotonicity assumption. Compared with Nash-Moser iteration in [5], the data do not require high regularity.
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