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Stability of large amplitude Ekman-Hartmann boundary layers in MHD: the case of ill-prepared data. (English) Zbl 1075.76033
Summary: We study an incompressible highly rotating fluid submitted to a high magnetic field between two planes with a Dirichlet boundary condition. We investigate the nonlinear stability of Ekman-Hartmann boundary layers under a spectral assumption for general initial data; this means that the data can be chosen as an arbitrary (but smooth enough) three-dimensional divergence-free vector field independent of the small parameter.

MSC:
76E25 Stability and instability of magnetohydrodynamic and electrohydrodynamic flows
76E07 Rotation in hydrodynamic stability
76E30 Nonlinear effects in hydrodynamic stability
76W05 Magnetohydrodynamics and electrohydrodynamics
76U05 General theory of rotating fluids
35B35 Stability in context of PDEs
35Q35 PDEs in connection with fluid mechanics
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