Analysis Seminar

Free-Boundary Magnetohydrodynamics Equations with Surface Tension

Chenyun Luo, The Chinese University of Hong Kong

Friday, October 29th, 2021
8:00 AM - 9:00 AM
Zoom ID 783 353 8838

We survey some recent progress in the study of the free-boundary problem in MHD equations describing the motion of a conducting fluid in an electromagnetic field under the influence of surface tension. We prove the 3D local well-posedness of this model in the appropriately Sobolev spaces. This is no easy consequence of the free-boundary Euler equations due to the strong coupling structure between the velocity and magnetic fields. In addition to adapting the method developed by Coutand and Shkoller to generate an approximate problem with artificial viscosity, we need to exploit the structure of the equations verified by the magnetic field to obtain a suitable energy functional that ties to the local existence. If time permits, we show that the aforementioned energy functional can be modified so that the energy estimate is uniform in the surface tension coefficient. This allows us to study the zero surface tension limit which yields the solution to the free-boundary MHD equations without surface tension given the physical sign condition is assumed.

Event contact: dan dot geba at rochester dot edu