活動時間：2024-09-08 08:30
活動地點：2号學院樓2202報告廳
主講人：Vladimir Chepyzhov
主講人中文簡介：
V. Chepyzhov研究員（科學博士）作為無窮維動力系統蘇聯學派著名數學家M.Vishik教授的代表性學生之一，是國際上無窮維動力系統領域的傑出學者和新一代的代表學者之一。現任俄羅斯科學院信息傳輸問題研究所首席科學研究員。主要從事無窮維動力系統吸引子理論的研究，特别是在一緻吸引子和軌道吸引子的基礎理論方面做出了奠基性以及深刻創新的工作，與M. Vishik教授共同撰寫的專著是本領域的經典著作之一，到目前發表學術論文95篇（數據來源于MathSciNet數據庫），被引用文獻次數達2198次。其中多篇論文都發表在Comm. Pure Appl. Math.，J. Math. Pures Appl.，Indiana Univ. Math. J.，Russian Math. Surveys等國際頂尖學術期刊上。
活動内容摘要：
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：孫春友