活动时间：2024-09-08 08:30
活动地点：2号学院楼2202报告厅
主讲人：Vladimir Chepyzhov
主讲人中文简介：
V. Chepyzhov研究员（科学博士）作为无穷维动力系统苏联学派著名数学家M.Vishik教授的代表性学生之一，是国际上无穷维动力系统领域的杰出学者和新一代的代表学者之一。现任俄罗斯科学院信息传输问题研究所首席科学研究员。主要从事无穷维动力系统吸引子理论的研究，特别是在一致吸引子和轨道吸引子的基础理论方面做出了奠基性以及深刻创新的工作，与M. Vishik教授共同撰写的专著是本领域的经典著作之一，到目前发表学术论文95篇（数据来源于MathSciNet数据库），被引用文献次数达2198次。其中多篇论文都发表在Comm. Pure Appl. Math.，J. Math. Pures Appl.，Indiana Univ. Math. J.，Russian Math. Surveys等国际顶尖学术期刊上。
活动内容摘要：
In the report, we study the limit as \alpha \to 0 of the long-time dynamics for various approximate alpha-models of a viscous incompressible fluid and their relation to the final dynamics of the exact 3D Navier-Stokes system. The alpha-models under consideration are divided into two classes depending on the orthogonality properties of the nonlinear terms of the equations of a particular alpha -model. We show that the trajectory attractors of alpha -models of class I have stronger properties of attraction for the trajectories than the attractors of alpha -models of class II. We prove that for both classes the bounded families of trajectories of the alpha -models under consideration converge in the corresponding weak topology to the trajectory attractor A_0 of the exact 3D Navier-Stokes system as time t tends to infinity. Furthermore, we establish that the trajectory attractor A_ \alpha of every alpha -model converges in the same topology to the attractor A_0 as \alpha \to 0. We construct the minimal limits Amin \to A0 of the trajectory attractors A_ alpha for all alpha -models as \alpha \to 0. We prove that every such set Amin is a compact connected component of the trajectory attractor A_0, and all the Amin are strictly invariant under the action of the translation semigroup.
主持人：孙春友