instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
Existence and uniqueness questions for the MHD equations
Conversaciones Fluidas
Fecha: Del 21.03.2017 al 23.03.2017 De 12.30 a 14.00
Lugar: Seminario I (IMUS), Edificio Celestino Mutis

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.