报告题目 Title：Lectures on nonuniqueness and norm inflation in PDEs

报告人 Speaker：罗肖雨滔 副教授

报告人所在单位 Affiliation：中国科学院晨兴数学中心

时间 Time：2025-11-03 15:00-16:30 (Lecture 1)

      2025-11-05 9:30-11:00 (Lecture 2)

地点 Venue：光华楼东主楼1601

报告摘要 Abstract：

Lecture 1. Nonuniqueness of linear transport equations with Sobolev vector fields

We discuss recent advances in the construction of nonunique solutions to linear transport equations. Since the seminal work of DiPerna-Lions, it has remained an open problem whether the the range of uniqueness guaranteed by their renormalization theory is sharp. In this lecture, we review recent progress from two complementary perspectives:  Eulerian approaches based on convex integration and Lagrangian approaches that construct solutions by hand.”

Lecture 2. Norm inflation for the Navier-Stokes equations in supercritical spaces

We demonstrate that the incompressible 3D Navier-Stokes equations exhibit norm inflations in supercritical spaces. The construction covers almost the entire range of spaces near the critical scaling exponent, including H^s for s<1/2. The underlying growth mechanism is driven by mixing or unmixing effects, depending on the sign of the derivative index.

个人简介 Bio：Prof. Xiaoyutao Luo is currently an associate professor at the Morningside Center of Mathematics, Chinese Academy of Sciences. He received his Ph.D. from University of Illinois at Chicago in 2020 and was an Elliott Assistant Research Professor at Duke University from 2020 to 2023. His current research is focused on PDEs arising from fluid dynamics. His research works have been published in Invent. Math., CPAM, ARMA, Ann. PDE, Anal. PDE etc.

海报Poster：罗肖雨滔 学术报告.jpg