Local existence of solutions to the 2D MHD boundary layer equations without monotonicity in Sobolev space

• Published in: AIMS mathematics Vol. 9; no. 3; pp. 5294 - 5329
• Main Author: Dong, Xiaolei
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2024
• Subjects: mhd boundary layer equations; the energy method; the existence of solutions; the weighted sobolev space
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2024256

In this work, we investigated the local existence of the solutions to the 2D magnetohy-drodynamic (MHD) boundary layer equations on the half plane by energy methods in weighted Sobolev space. Compared to the existence of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays an important role, we used the initial tangential magnetic field with a lower bound $ \delta > 0 $ instead of the monotonicity condition of the tangential velocity.