- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:04
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
16
2014
3
Global existence and decay for solutions of the Hele–Shaw flow with injection
C.H. Arthur
Cheng
National Central University, JHONGLI CITY (TAOYUAN), TAIWAN
Daniel
Coutand
Heriot-Watt University, EDINBURGH, UNITED KINGDOM
Steve
Shkoller
University of Oxford, OXFORD, UNITED KINGDOM
Hele–Shaw, interface problems, stability, Hele–Shaw free boundary problems, surface tension
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.
Partial differential equations
Fluid mechanics
297
338
10.4171/IFB/321
http://www.ems-ph.org/doi/10.4171/IFB/321