报告题目：Stabilizing Mechanisms for the 2D Navier–Stokes Equations with Horizontal Dissipation

主 讲 人：Jiahong Wu 教授（University of Notre Dame）

报告时间：2026年9月14日（周一）上午10:00-12:00

报告地点：#腾讯会议：416-466-171 密码：314256

报告摘要：The 2D Navier–Stokes equations with dissipation in only the horizontal direction sit between two very different regimes. With full dissipation, solutions on the whole space R^2 are stable near the trivial solution and decay algebraically in time. Without any dissipation, solutions to the 2D Euler equations can grow rapidly in Sobolev norms. In the intermediate case of purely horizontal dissipation on the whole space R^2, neither the stability near the trivial solution nor the large-time behavior is currently understood. This talk describes three mechanisms that help stabilize the horizontally dissipated 2D Navier--Stokes system. The first is a weakening of the dissipation itself: we prove that the equations with fractional horizontal dissipation $\Lambda_1^{2s}$ ($0 \le s < 1$) are stable, together with explicit decay rates (joint with Z. Wang and N. Zhu). The second is buoyancy: coupling the horizontally dissipated velocity to a temperature equation in the Boussinesq system, we establish global stability and enhanced decay, where the interplay of anisotropic dissipation and anisotropic dispersion is the driving mechanism (joint with M. Yan and N. Zhu). The third is a background magnetic field: coupling the system to the magnetic field in a 2D MHD system with only horizontal dissipation and magnetic diffusion, we prove global stability near a background magnetic field. Reformulating the system in Els\"asser-type variables reveals an intrinsic dispersive interaction between the two coupled fields, and the analysis uncovers a hidden nonlinear dissipative structure generated by the background field and the coupling (joint with M. Yan, N. Zhu, and Y. Zhu).

个人简介：吴家宏教授1988年本科毕业于北京大学数学科学学院，1996年在美国芝加哥大学获得博士学位，师从世界著名数学家Peter Constantin院士。先后工作于美国普林斯顿高等研究院，美国德州大学奥斯汀分校，现为美国圣母大学教授。吴家宏教授长期致力于非线性流体动力学方程的理论研究，在Navier-Stokes方程，SQG方程，Boussinesq方程和MHD方程等数学前沿问题的研究上做出了一系列重要贡献，先后在国际一流的学术刊物 CPAM、CMP、ARMA、Math. Ann.、Adv. Math、JFA、SIAM、AIHP、CPDE、JDE等发表学术论文170余篇，论文被国际同行引用超过7000次。