报告题目 Title：Asymptotically Self-Similar Blowup for 3D Incompressible Euler with $C^{1, 1/3-}$ Velocity

报告人 Speaker：陈嘉杰

报告人所在单位 Affiliation：University of Chicago

时间 Time：2026-08-28 9:00-11:30

地点 Venue：Room 1801, Guanghua Eastern Main Tower, Fudan University (Handan Campus)

报告摘要 Abstract：Whether the incompressible Euler equations in $R^3$ can develop a finite-time singularity from smooth initial data is a long-standing open problem in mathematical fluid mechanics. In the axisymmetric setting without swirl, global regularity is known for $C_c^\alpha$ initial vorticity for all $\alpha \geq 1/3$. Below this regularity threshold, for any $\alpha \in (0,1/3)$, we construct exact $C^\alpha$ self-similar blowup profiles for the vorticity of the 3D axisymmetric Euler without swirl, and build on them to prove asymptotically self-similar blowup from $C_c^\alpha$ initial vorticity and $C^{1,\alpha} \cap L^2$ initial velocity. Moreover, we provide a complete characterization of the limiting behavior of these $C^\alpha$ vorticity profiles and the associated blowup solutions as $\alpha$ tends to $1/3$. Our construction is based on lifting $C^\infty$ blowup profiles for a 1D nonlocal model and exploits the anisotropy of the 3D self-similar flow. To the best of our knowledge, our results provide the first example in which a singularity from a genuinely 1D nonlocal fluid model is lifted to construct blowup for incompressible fluid equations in $R^2$ or $R^3$.

个人简介 Bio：Jiajie Chen is an Assistant Professor in the Department of Mathematics at the University of Chicago. He received his Ph.D. in Applied and Computational Mathematics from Caltech under the supervision of Thomas Y. Hou. From 2022 to 2025, he was a Courant Instructor at New York University. His research focuses on singularity formation in nonlinear partial differential equations, particularly those related to mathematical fluid mechanics.

海报 Poster: 陈嘉杰 学术报告.jpg