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Co-authors: Van-Sang Ngo
Abstract: In this joint work with Van-Sang Ngo, we consider the 3D-rotating magnetohydrodynamic (MHD) system.
We begin this talk by providing a few examples of penalized geophysical models similar to the incompressible Navier-Stokes system, and which converge (when the small penalization parameter goes to zero) towards a limit system that can be easily seen to be incomplete. Reaching a more complete limit requires adding to some classical initial data a non-conventional component linked to the special structure of the limit system.
Then we study (for both weak and strong solutions) the asymptotics when the Rossby number goes to zero (i.-e. for strong rotation) of the 3D-rotating (MHD) system when the initial velocity and magnetic field both feature some 2D-part (i.-e. depending only on the horizontal space variables).
We show this limit is the 2D-MHD system with three components supplemented with an additional 3D magnetic field transported by the 2D limit velocity.