数学研究所

数学科学全国重点实验室

学术报告

偏微分方程研讨班

Speaker: Professor Amaury Hayat（CERMICS - Ecole des Ponts Institut Polytechnique de Paris）
Inviter: 张平 院士
Language: English
Title: Stabilization of PDEs and AI for mathematics 
Time&Venue: 2025年7月24日（星期四）15:00-16:00 & 南楼N913

Abstract: This talk will discuss new methods and perspectives in stabilization. First, we'll look at the stabilization problem for PDEs from an abstract perspective and present an approach called F-equivalence. The principle is simple: instead of directly trying to find a feedback control that makes the system stable, we seek to find a feedback control that transforms the system under consideration into a simpler system, for which stability is already known. We'll come back to the progress made with this method over the last years. Secondly, we'll look at a more concrete problem: the stabilization of hyperbolic equations modeling road traffic. We'll show how abstract mathematical concepts, such as entropic solutions, can have tangible impacts in real-life scenarios, and we'll discuss the application to traffic regulation and the reduction of accordions in traffic jams. Finally, we'll discuss recent advances in AI for mathematics and, in particular, how to train AI to have mathematical intuition to help solve problems. 

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偏微分方程研讨班
Speaker: Dr. YANG Haocheng（Université Paris-Saclay ） 
Inviter: 张平 院士
Language: English
Title: Global well-posedness of a 2D fluid-structure interaction problem without dissipation  
Time&Venue: 2025年7月24日（星期四）16:00-17:00 & 南楼N913
Abstract: In this talk, we will analyze the incompressible Euler equation in a time-dependent 2D fluid domain, whose interface evolution is governed by the law of linear elasticity without damping. Our main result asserts that the Cauchy problem is globally well-posed in the energy space for irrotational initial data without any smallness assumption. We also prove the continuity with respect to the initial data and the propagation of regularity. In the absence of parabolic regularization, a key ingredient in our analysis is a novel reduction to a nonlinear Schrödinger-type equation, allowing us to apply dispersive estimates. To carry this out, we develop new estimates for the Dirichlet-to-Neumann operator in low-regularity regimes through tools from classical harmonic analysis and paradifferential calculus. This is a joint work with Thomas Alazard and Chengyang Shao.