勷勤数学•专家报告

题      目：Exponential stability of a free boundary problem with spherical symmetry for a gas bubble immersed in a bounded incompressible liquid

报  告  人：罗涛 教授  (邀请人：罗天文)

                                 香港城市大学

时      间：11月17日  10：30-11：30

地     点：数科院西楼114教室

报告人简介:

       罗涛，香港城市大学教授。1995年于中国科学院数学研究所获得博士学位。后于美国密西根大学 (University of Michigan) 、乔治城大学 (Georgetown University) 历任助理教授、副教授及教授。2016年至今于香港城市大学任教授。罗涛教授的主要研究领域为流体力学中的非线性偏微分方程，如 Euler 及 Navier-Stokes 方程，输运方程等。研究成果发表于 Comm. Pure Appl. Math., Arch. Rational Mech. Anal., Comm. Math. Phys., Adv. Math.等学术刊物。

摘      要：

       This talk is mainly concerned with the free boundary problem for an approximate model of a gas bubble of finite mass enclosed within a bounded incompressible viscous liquid, accounting for surface tensions at both the gas-liquid interface and the external free surface of the entire gas-liquid region. It is found that any regular spherically symmetric steady-state solution is characterized by a positive root of a ninth-degree polynomial for which the existence and uniqueness are proved and a one-to-one correspondence between equilibria and pairs of gas mass and liquid volume is established, by a rescaling argument. We prove that these equilibria exhibit nonlinear and exponential asymptotic stability. Moreover, we construct a global center manifold. Furthermore, we derive the optimal exponential decay rate for small liquid volumes by analyzing the spectrum bounds of the associated linear operator, This talk is based on joint work with Chengchun Hao and Siqi Yang.

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