Non-linear hyperbolic equations and related topics
timetable:
Fri 7 Sep, 9:00 - 10:00, Aula Dini
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seminar: Long-time Sobolev stability for small solutions of quasi-linear Klein-Gordon equations on the circle
speaker: Jean-Marc Delort (Département de Mathématiques, Université Paris 13)abstract: The goal of the talk will be to prove that higher Sobolev norms of solutions of quasi-linear Klein-Gordon equations with small Cauchy data on the circle remain small over intervals of time longer than the ones given by local existence theory. This result extends previous ones obtained by several authors in the semi-linear case. The main new difficulty one has to cope with is the loss of one derivative coming from the quasi-linear character of the problem. The main tool used to overcome it is a global paradifferential calculus adapted to the Sturm-Liouville operator with periodic boundary conditions.
timetable:
Fri 7 Sep, 9:00 - 10:00, Aula Dini
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