Martes 21 y Jueves 23
The idea of magnetic relaxation (dating back to Arnold and Moffatt) applies to the non-resistive MHD equations, providing a mechanism for the construction of solutions to the Euler equations with non-trivial topology.
In these lectures we discuss existence and uniqueness questions for the systems, focusing on the new tools that need to be developed to consider the optimal regularity. Some of his topics include:
- generalised Ladyzhenskaya inequalities,
- maximal regularity theory
- new commutator estimates (and counter-examples in the critical Sobolev space)
- Analysis on Besov spaces (for the critical regularity)
The presented work corresponds to various collaborations with J.Y. Chemin, C. Fefferman, D. McCormmick and J.C. Robinson.