报告人：王荣年（上海师范大学）  

邀请人：李骥

报告时间：2021年11月2日（星期二）14:00-15:30

报告地点：腾讯会议 ID：856 503 577

报告题目：The Invariant Manifold Approach Applied to the Study of Hyperdissipative Navier-Stokes Equations in High Dimensions

报告摘要：Consider the incompressible hyperdissipative Navier-Stokes equations\begin{equation*}\left\{\begin{array}{ll}u_t+\epsilon(-\Delta)^\alpha u+(u\cdot\nabla)u+\nabla p=f,\\\nabla\cdot u=0\end{array}\right.\end{equation*}on a 2D or 3D periodic torus, where the power $\alpha\geq {3}/{2}$ and the forcing function $f$ is time-dependent. We intend to reveal how the fractional dissipation $(-\Delta)^\alpha$ affects long-time dynamics of weak solutions. Precisely, we prove that there exists a finite-dimensional Lipschitz manifold being {locally {forward} invariant and} pullback exponentially attracting. Moreover, the compact uniform attractor is contained in the union of all fibers of the manifold. No large viscosity $\epsilon$ is assumed. It is also significant that in the 3D case the spectrum of the fractional Laplacian $(-\Delta)^{3/2}$ does not have arbitrarily large gaps.  

报告人简介：王荣年, 上海师范大学教授, 博士生导师（应用数学）。目前主要从事非线性发展方程适定性、多值扰动及解集的拓扑正则性、不变流形理论等问题的研究, 完成的研究结果已被"Mathematische Annalen"、“Int. Math. Res. Notices 、"Journal of Functional Analysis"、"Journal of Differential Equations"" Journal of Phys. A: Math. Theo."等学术期刊发表. 主持承担了2项国家自然科学基金面上项目、国家自然科学基金青年项目、4项省自然科学基金项目和2项省教育厅基金项目。