京师数学前沿论坛 第十三讲
京师数学前沿论坛
报告题目(Title)：On a generalization of the Bardos-Tartar conjecture to nonlinear dissipative PDEs
报告人(Speaker)：Prof. Edriss S. Titi （University of Cambridge and The Weizmann Institute of Science）
地点(Place)：后主楼1124
时间(Time)：2025年12月30日下午16:00-17:00
报告摘要
In this talk I will show that every solution of a KdV-Burgers-Sivashinsky type equation blows up in the energy space, backward in time, provided the solution does not belong to the global attractor. This is a phenomenon contrast to the backward behavior of the 2D Navier-Stokes equations, subject to periodic boundary condition, studied by Constantin, Foias, Kukavica and Majda, but analogous to the backward behavior of the Kuramoto-Sivashinsky equation discovered by Kukavica and Malcok. I will also discuss the backward behavior of solutions to the damped driven nonlinear Schrdinger equation, the complex Ginzburg-Landau equation, and the hyperviscous Navier-Stokes equations. In addition, I will provide some physical interpretation of various backward behaviors of several perturbations of the KdV equation by studying explicit cnoidal wave solutions. Furthermore, I will discuss the connection between the backward behavior and the energy spectra of the solutions. The study of backward behavior of dissipative evolution equations is motivated by a conjecture of Bardos and Tartar which states that the solution operator of the two-dimensional Navier-Stokes equations maps the phase space into a dense subset in this space.
主讲人简介
Edriss S. Titi. Holds the Nonlinear Mathematical Sciences Professorial Chair at the University of Cambridge, UK. He is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics, the John Simon Guggenheim Memorial Foundation, USA, and the Institute of Physics, UK. He is recipient of many international awards including the Humboldt Research Award and the Einstein Visiting Fellow, Germany. Titi’s research in applied and computational mathematics lies at the interface between rigorous applied analysis and physical applications. Specifically, in studying the Euler, Navier-Stokes, and other related geophysical and turbulence models.
