Global solutions to the incompressible ideal MHD (I)(II)
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：Yuan Cai (Fudan University)
： 2024-11-20 15:00
：Conference Room S105 & S107 at Experiment Building at Haiyun Campus
Speaker：Yuan Cai (Fudan University)
Time：2024-11-20 & 2024-11-21, 15:00
Location：Conference Room S105 & S107 at Experiment Building at Haiyun Campus
Abstract:
This series talks consist of two parts. In the first part, we study the Cauchy problem of the incompressible ideal (inviscid and non-resistive) magnetohydrodynamics. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero constant state are sufficiently small in certain weighted Sobolev spaces, we show the global in time existence of solutions.
In the second part, we study the global current-vortex sheets in the two-dimensional ideal incompressible MHD. The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal incompressible magnetohydrodynamics under the strong horizontal background magnetic field. This appears to be the first result on the global solutions of the free boundary problems for the ideal (inviscid and non-resistive) incompressible rotational fluids. These are based on the joint works with Professor Zhen Lei.
