报告人简介：
李新华博士，现为兰州大学数学与统计学院副教授，硕士生导师，主要从事无穷维动力系统吸引子与惯性流形相关问题的研究。先后获得国家自然科学基金青年基金，博士后面上基金，甘肃省青年基金的资助。曾获甘肃省优秀博士学位论文。在惯性流形、奇异耗散系统吸引子等相关研究中取得一些成果，部分成果已发表在SIAM J. Math. Anal.，J. Differential Equations, Proc. Amer. Math. Soc.等期刊。
报告摘要：
The dissipative infinite-dimensional dynamical systems can be reduced to finite-dimensional ordinary differential equations by the restriction to inertial manifolds. While the construction of inertial manifolds strongly relies on the so-called spectral gap condition, which greatly restricts some applications. For example, whether the 2D Navier-Stokes equations (NSEs) enjoys a finite-dimensional reduction via an inertial manifold has remained an open question since the mid-1980’s. Spatial averaging principle is an alternative method to construct inertial manifolds for the case where the so-called spectral gap condition is violated. In this talk, we first introduce the main idea on how to establish an inertial manifold via spatial averaging method. Subsequently, we will show our recent theoretical extensions of this methodology and demonstrate its some applications in modified NSEs and other PDEs models.
