报告题目 Title：Well-posedness theory of the Navier-Stokes and Euler equations: long-standing challenges and some recent progress

报告人 Speaker：任潇，博雅博士后

（主持人 Host：赵东元 院士）

时间 Time：2025-03-24 15:30 - 16:30

地点 Venue：光华楼东辅楼101多功能厅

报告摘要 Abstract：The Navier-Stokes and Euler equations form the cornerstone of fluid dynamics. This talk is concerned with three fundamental challenges in the mathematical analysis of these equations-namely, the global regularity of incompressible Navier-Stokes flows (a Millennium Problem), the Leray problems for stationary Navier-Stokes equations, and the hydrodynamic stability of Euler flows. I will present our recent progress on these problems, including:

(1) Quantitative partial regularity theory, improving the classical result of Caffarelli-Kohn-Nirenberg (1982)

(2)A geometric characterization of potential singularities, which extends the paradigm of Constantin-Fefferman (1993) connecting vorticity alignment and regularity

(3)A complete well-posedness theory for the 2D stationary Navier-Stokes equations at small Reynolds numbers

(4) Global stability of the “rigid body rotational solution to the 3D Euler equations

个人简介 Bio：2018 年在复旦大学获学士学位，2023 年在复旦大学获博士学位。2023-2025 年在北京大学开展博士后研究，期间获得博新计划资助。现从事偏微分方程和数学物理研究。与合作者创新性提出Navier-Stokes 方程的定量部分正则性理论，解决二维稳态绕流问题的唯一性,证明 Euler 方程一致旋转解的整体稳定性等。在Advances in Mathematics、Mathematische Annalen、Communications in Mathematical Physics (2篇)、Archive for Rational Mechanics and Analysis等国际期刊上发表论文8 篇。曾获全国偏微分方程优秀博士论文奖、复旦大学优秀博士学位论文、复旦大学“学术之星”特等奖等。

海报 Poster：会议海报.jpg会议内容与报告人介绍.jpg