标题：The stability of the Hele-Shaw flow with and without surface tension and injection

报告人：郑经斅教授（台湾中央大学）

地点：数学与计算机科学学院4号楼229室

时间：2018年3月7日下午4：00-5：00

摘要：We examine the stability and decay of the free boundary perturbations in a Hele-Shaw cell under the injection 

 

of fluid. In particular, we study the perturbations of spherical boundaries as time t \o \\infty. In the presence 

 

of positive surface tension, we examine both slow and fast injection rates.When fluid is injected slowly, the 

 

perturbations decay back to an expanding sphere exponentially fast, while for fast injection, the perturbation 

 

decays to an expanding sphere with an algebraic rate. In the absence of surface tension, we study the case of a 

 

constant injection rate, and prove that perturbations of the sphere decay like (1+t)^{-0.5+\\epsilon) for \\epsilon > 

 

0 small.

 

郑经斅 台湾中央大学教授,流体力学数学理论领域专家，目前在一流杂志《Comm. Pure Appl. Math.》, 《Proceedings of the 

 

National Academy of Sciences of the United States of America》，《Adv. Math.》,以及高水杂志《SIAM J. Math. Anal.》

 

， 《Comm. Partial Differential Equations》, 《J. Math. Fluid Mech.》等发表多篇论文。