报告人：罗涛 教授 (香港城市大学)

时间：2025年09月14日 10:00-

地点：理科楼LA103

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.

邀请人：王华桥

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