GLOBAL-IN-TIME STABILITY OF 2D MHD BOUNDARY LAYER IN THE PRANDTL-HARTMANN REGIME

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)5749-5760
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume50
Issue number6
Online published6 Nov 2018
Publication statusPublished - 2018

Abstract

In this paper, we prove the global existence of solutions with analytic regularity to the 2D magnetohydrodynamic (MHD) boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multiscale expansion in [D. Gerard-Varet and M. Prestipino, Z. Angew. Math. Phys., 68 (2017), 76]. The analysis shows that the combined effect of the magnetic diffusivity and transverse magnetic field on the boundary leads to a linear damping on the tangential velocity field near the boundary. And this damping effect yields the global-in-time analytic norm estimate in the tangential space variable on the perturbation of the classical steady Hartmann profile.

Research Area(s)

  • MHD boundary layer, Prandtl-Hartmann regime, global stability, analytic regularity, NAVIER-STOKES EQUATION, ZERO VISCOSITY LIMIT, WELL-POSEDNESS, ILL-POSEDNESS, ANALYTIC SOLUTIONS, MAGNETIC-FIELD, HALF-SPACE, EXISTENCE, SYSTEM, EULER