# Mathematics Colloquia and Seminars

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### The nonlinear stability of Alfven waves

**PDE and Applied Math Seminar**

Speaker: | Pin Yu, Yau Mathematical Sciences Center, Tsinghua University |

Location: | 3106 MSB |

Start time: | Thu, Feb 2 2017, 4:10PM |

We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. 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.