勷勤数学•专家报告

题      目：Flexibility through moving vortices 3D Navier–Stokes and SQG

报  告  人： Quoc-Hung NGUYEN 副研究员  (邀请人：袁源)

                                              中国科学院数学与系统科学研究院

时      间： 10月6日  14：00-15:00

地     点：数科院西楼111报告厅

报告人简介:

          Prof. Quoc-Hung NGUYEN is currently an Associate Professor at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences (CAS), Beijing, China. He obtained my Ph.D. in Mathematics from Laboratoire de Mathématiques et Physique Théorique, Université de Tours, France in 2014.

Research interests: Partial Differential Equations and Analysis. 

摘      要：

         We use moving localized vortices to construct flexible weak solutions of the three-dimensional incompressible Navier–Stokes equations and the inviscid surface quasi-geostrophic (SQG) equation on periodic domains. Their motion cancels the leading self-interaction, while time averaging reconstructs the Reynolds stress.

For Navier–Stokes, rescaled Hill vortices produce solutions in \(C_tL_x^2\) with gradients in \(C_tL_x^{6/5+\varepsilon_{\mathrm{NS}}}\). For SQG, localized traveling profiles yield momentum weak solutions with \(\theta\in C_tL_x^{4/3+\varepsilon_{\mathrm{SQG}}}\), for explicit positive exponents. These solutions approximate arbitrary admissible initial and terminal states, and time localization yields nonuniqueness for a dense set of initial data.

The talk emphasizes the construction and its main analytical challenges: controlling viscosity and crossing the concentration threshold for Navier–Stokes, and handling the nonlocal SQG interaction through a bilinear null-form estimate.

This talk is based on joint works with Elia Bruè and Rui Jin; with Zexi Wang.

          欢迎老师、同学们参加、交流！