Speaker: Professor Nicolas Burq，Université Paris-Saclay

Inviter: 张平院士

Title: Nonlinear interpolation and the flow map of quasilinear equations

Language: English

Time & Venue: 2025.06.18 15:00-17:00 南楼N913

Abstract: Solving a quasilinear evolution Partial Differential Equation requires usually two quite distinct steps: first implementing an iteration scheme where some high regularity norms are bounded and second implementing a contraction scheme at some lower regularity level. This double scheme implies existence of the solution at the high regularity level and continuity of the flow (i.e. the data-to-solution map) at the low regularity level. Starting from this point many works have been dealing with recovering the continuity of the flow at the high regularity level. In this talk, I will present an abstract interpolation result which shows that actually this continuity property of the flow follows automatically from the estimates that are usually proven when establishing the existence of solutions: propagation of regularity via tame {\em a priori} estimates for higher regularities and contraction for weaker norms.I will illustrate on some simple examples (burger’s equations and nonlinear Schrödinger equations) the robustness of the approach. This is a joint work with T.Alazard, M. Ifrim, D. Tataru and C. Zuily.