Magnetic effects on the solvability of 2D incompressible magneto-micropolar boundary layer equations without resistivity in Sobolev spaces. (November 2022)

• Record Type: Journal Article
• Authors: Zou, Lin; Lin, Xueyun
• Is Part Of: Nonlinear analysis. Volume 224(2022)
• Publication Date: 2022-11
• Subjects: Magneto-micropolar boundary layer -- Well-posedness -- Ill-posedness -- Sobolev spaces -- General decay; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113080
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we consider the magnetic effect on the Sobolev solvability of the two-dimensional incompressible magneto-micropolar boundary layer system without resistivity. This gives a complement to the previous work of Lin et al. (2022), where the well-posedness and the convergence theory were established for the magneto-micropolar boundary layer system without monotonicity in Sobolev spaces. If the initial tangential magnetic field is not degenerate, a local-in-time well-posedness theory in Sobolev spaces is established without the monotonic condition on the velocity or the micro-rotational velocity. Moreover, when the tangential magnetic field of shear layer degenerates at the non-degenerate critical point of the initial velocity and the initial micro-rotational velocity, the linearized magneto-micropolar boundary layer system around a shear flow with general decay is ill-posed in Sobolev spaces.