On the ideal magnetohydrodynamics in three-dimensional thin domains: well-posedness and asymptotics

In this talk, I will first give a short introduction and survey on MHD. Then I will talk about my recent work on the ideal MHD subjected to a strong magnetic field along $x-1$ direction in three-dimensional (3D) thin domain with slip boundary conditions. The main results include the global well-posedness and the asymptotics of MHD from the thin domain to the plane when the thickness of the domain goes to zero. The proofs of main results rely on the design of the proper energy functional and the null structures of the nonlinear terms.