On the geometrical structure of certain equations of hydrodynamical type
Résumé
It is well-known that some PDEs of hydrodynamical like KdV, CH, DP, HS, CLM, ... have a rich geometrical structure. In the first part of my talk, I will give a survey on this general geometric framework, namely metric and non-metric Euler equation on diffeomorphisms group. In the second part, I will consider more analytical questions like the smoothness of the spray and local existence of geodesics.