We plan to give three talks on our recent joint work on nonlinear stability of Alfven waves in magnetohydrodynamics (MHD). We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity in a strong magnetic background. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts: the solution at the beginning behave like non-dispersive waves and the shape of the solution persists for a very long time (proportional to the Reynolds number); thereafter, the solution will be damped due to the long-time accumulation of the diffusive effects; eventually, the total energy of the system becomes extremely small compared to the viscosity so that the diffusion takes over and the solution afterwards decays fast in time. We do not assume any symmetry condition. The size of data and the a priori estimates do not depend on viscosity. The proof is built upon a novel use of the basic energy identity and a geometric study of the characteristic hypersurfaces. The approach is partly inspired by Christodoulou-Klainerman's proof of the nonlinear stability of Minkowski space in general relativity.
　　The first talk (15:00--15:50) given by XU Li will review some recent advances on MHD systems.
　　The second talk (16:05--16:55) given by YU Pin will sketch a construction of global solutions for 3-D ideal incompressible MHD systems.
　　The third talk (17:10--18:00) given by HE Lingbing will explain the idea to the global well-posedness and the decay mechanism for MHD systems with arbitrary small viscosity.