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Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium
Jiahong Wu, Oklahoma State University
Date & time: Tuesday, 24 November 2020 at 1:40PM - 3:40PM
Abstract: This talk presents the global existence and stability result on solutions near a background magnetic field to the 3D incompressible magnetohydrodynamic (MHD) system with horizontal dissipation and vertical magnetic diffusion. Due to the lack of the vertical dissipation and the horizontal magnetic diffusion, the stability problem concerned here is difficult and classical approaches no longer apply. This work exploits the extra smoothing and stabilizing effect in the wave structure resulting from the coupling and interaction of the velocity and the magnetic fields. By constructing a suitable energy functional to incorporate this stabilizing effect and employing the bootstrapping argument, we are able to show the desired existence and stability result.