报告时间：2025年6月3日（周二）下午3：30-4: 30
报告地点：国交二号楼（数统学院）315会议室
报告人：Nicolas Burq 教授 （Université Paris-Saclay 巴黎-萨克雷大学）
报告人简介：
尼古拉·比尔克（Nicolas Burq）是法国著名数学家，在分析和偏微分方程领域贡献卓著。他毕业于巴黎高等师范学院，1992年获巴黎第十一大学（现巴黎-萨克雷大学组成部分）博士学位，曾任法国国家科学研究中心（CNRS）研究员（1991-1998年，就职于巴黎综合理工学院），1998年起任巴黎第十一大学教授（现为巴黎-萨克雷大学）。
他现任巴黎-萨克雷大学奥赛（d'Orsay）数学实验室教授，并担任法兰西大学研究院高级成员。其研究涵盖微局部分析、控制理论、色散方程和非线性偏微分方程等领域。作为该领域的杰出学者，他曾在2010年国际数学家大会（ICM）作邀请报告。
此外，他在Acta Mathematica, Inventiones Mathematicae, Journal of the American Mathematical Society (JAMS), Duke Mathematical Journal, Geometric and Functional Analysis (GAFA).等顶级期刊发表论文一百余篇。
Abstract（摘要）：
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
