Title: Mathematical structure of hierarchies of reduced MHD models
Bruno Despres, UPMC

This presentation will show how to extend the theory of hyperbolic systems of conservation laws with constraints (à la "Chen-Levermore-Liu") in order to design  hierarchies of reduced MHD models in Tokamak geometry. The  first  result is  a systematic design of well-posed hierachies of  reduced MHD models. Here well-posed means that the system is endowed with a physically sound energy identity and that existence of a weak solution can be proved. The second result is perhaps more important for applications. It shows that  the growth rate of linear instabilities of the initial (non reduced) model is lower bounded by the growth rate of linear instabilities of the reduced model.
This work has been done with Rémy Sart.