Seminario EDPs y Mecánica de Fluidos

Mini-Course on Splash singularities for the free boundary ideal MHD equations I

Ponente:  Matthew Blair Hernández (ICMAT)
Fecha:  jueves 21 de octubre de 2021 - 12:00
Lugar:  Aula Naranja (ICMAT)


In this mini-course we discuss splash singularity formation  for the ideal incompressible MHD equations, a model of plasma dynamics, with a primary focus on the three-dimensional problem. We construct analytic splash singularities for the system with the use of an abstract Cauchy-Kovalevskaya theorem.

The splash singularity problem for the 3D MHD equations has many  unique features which require different techniques than those used in splash singularity constructions for other equations. In particular, there is nontrivial vorticity in the fluid region, there  is an electric field in the vacuum which interacts with the plasma,  and in three dimensions there is no longer a conformal change of variables we can use to convert our splash domain into a  non-self-intersecting one, as one usually does for 2D splashes.

On the other hand, we are still able to invert the relevant operators without such a change of variables, and the external electric field, which is not present in the water wave equations, actually helps us pull apart the splash.