学术报告（吴家宏 3.16）

Physical experiments and numerical simulations have demonstrated that background magnetic fields stabilize electrically conducting fluids. This talk presents well-posedness and stability results that establish these observations as mathematically rigorous facts on several magnetohydrodynamic (MHD) systems. The first MHD system focused here couples a 2D incompressible Euler-like equation for the velocity with a diffusive induction equation for the magnetic field. The Euler equation has an extra Riesz transform term and itself is not known to be well-posed or stable. However, we are able to show the global well-posedness near a background magnetic field for the MHD system.  The second MHD system presented here is a 3D incompressible MHD system.  The velocity in this MHD system satisfies the 3D anisotropic Navier-Stokes equations with dissipation in only one direction, which is not known to be globally well-posed. We present a recent global well-posedness and stability result on this 3D MHD system.