Global existence and decay for solutions of the Hele-Shaw flow with injection

Please use this identifier to cite or link to this item: https://ir.lib.ncu.edu.tw/handle/987654321/109223

Title:	Global existence and decay for solutions of the Hele-Shaw flow with injection
Authors:	鄭經斅;Cheng, C.H. Arthur;Coutand, Daniel;Shkoller, Steve
Contributors:	理學院數學系
Keywords:	Analysis;Boundary value problems;Flow (Dynamics);Fluid mechanics;Partial differential equations
Date:	2014-01-01
Issue Date:	2026-04-23 16:16:30 (UTC+8)
Publisher:	Zuerich, Switzerland: European Mathematical Society Publishing House
Abstract:	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 \to +\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)^{-1/2+ \epsilon }$ for $ \epsilon >0$ small. 其他題名： Interfaces Free Bound 出版者： Zuerich, Switzerland: European Mathematical Society Publishing House 出版日期： 2014-01-01 出處： Interfaces and free boundaries, 2014-01, Vol.16 (3), p.297-338 版權： European Mathematical Society 版權： COPYRIGHT 2014 European Mathematical Society Publishing House 識別號： ISSN: 1463-9963 識別號： EISSN: 1463-9971 識別號： DOI: 10.4171/IFB/321
Appears in Collections:	[Department of Mathematics] journal & Dissertation

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