勷勤数学•专家报告

题      目：Dispersion and singular limit of 2D rotating Navier-Stokes-Korteweg equations

报  告  人：魏正珍 教授  (邀请人：叶伟奎)

                                       暨南大学

时      间： 10月15日  15:00-16:00

地     点：数学科学学院西楼 114

报告人简介:

        魏正珍现为暨南大学数学系讲师。先后在兰州大学、中山大学获得学士 、博士学位，2021-2023年在北京应用物理与计算数学研究所从事博士后工作。 主要研究方向为可压缩流体解的衰减估计和大气海洋模型的奇异极限理论，在 Phys. D，JDE等SCI期刊上发表论文多篇。

摘      要：

        In this paper, we are concerned with the singular limit of local-in-time strong solutions of the Cauchy problem to Navier-Stokes-Korteweg equations with ill-prepared initial data as the Mach number and the Rossby tend to zero. We derive novel estimates to overcome the difficulties caused by the capillary effects. Subsequently, we investigate the asymptotic behavior of the system as the parameters tend to zero. A central focus of our analysis is to explore the dispersion phenomenon of the fast oscillating waves within the system. To facilitate this, we construct the Strichartz space-time decay estimates for the propagators by a refined study on the spectra of the large operator.

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