数学研究所

学术报告

偏微分方程研讨班

Speaker: 陈辉（浙江科技大学）

Inviter: 吴忠二 博士后

Language: Chinese

Title: The local regularity theory for the Stokes and Navier--Stokes equations near the curved boundary

Time&Venue: 2025.05.19 (星期一) 15:00-16:00

&南楼N224

Abstract: In this talk, we study local regularity of the solutions to the Stokes equations near the curved boundary under no-slip and slip boundary conditions.  As an application, we obtain the maximal regularity of the solution to the incompressible Navier--Stokes equations near boundary regular point.

---------------------------------------------------------------------------------------------

Speaker: Yao Xu（University of Chinese Academy of Sciences）

Inviter: 吴忠二 博士后

Language: Chinese

Title: Dimension estimate for attractors of wave equations with degenerate energy damping

Time&Venue:2025.05.19 (星期一) 16:00-17:00

& 南楼N224

Abstract: In this talk, we discuss about the fractal dimension of the global attractor of a class of wave equations with degenerate energy damping. In a general setting, we first establish the well-posedness of the problem and the existence of the global attractor. Then we propose a new idea to calculate the fractal dimension of the attractor, where the degeneration renders traditional methods of contraction and quasi-stability no longer applicable.