PDE seminar:Global existence of smooth solution of a 3D loglog energy-supercritical wave equation

2011-12-5 16:30 - 2011-12-5 18:00
Faculty of Science Building #3 Room 202
Tristan Roy (Kyoto University)
The global behavior of smooth solutions of super-critical problems is
poorly understood: this is mostly due to the lack of conservation laws in
high regularity Sobolev spaces. However, when the linearity is barely
supercritical (of a loglog type), it is possible to overcome this
difficulty. One first control a long time estimate by means of
concentration and an a priori bound of the norm of the solution in a high
regularity Sobolev space; then one finds an a posteriori bound of this norm
by combining the long time estimate with an induction on time of the
Strichartz estimates.

This seminar is co-hosted by the PDE seminar and the Wave seminar.