Local well-posedness of solutions to 2D magnetic Prandtl model in the Prandtl-Hartmann regine

2023/04/02 by Yuming Qin, Qin, Yuming, Xiuqing Wang +3
Mathematics · #35M13 #35Q35 #53C35 #76N10 #76N15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2304.00529

openalex publication_date 2023/04/02 · openalex created_date 2023/04/06 · openalex updated_date 2026/08/01

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 \cite[5], the data do not require high regularity.

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