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arXiv · 1208.6213

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

C. H. Arthur Cheng·Daniel Coutand·Steve Shkoller
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Abstract

We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere decay to zero exponentially fast. On the other hand, with a time-dependent rate of fluid injection into the Hele-Shaw cell, the distance from the moving boundary to an expanding sphere (with time-dependent radius) also decays to zero but with an algebraic rate, which depends on the injection rate of the fluid.

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C. H. Arthur Cheng, Daniel Coutand, Steve Shkoller. 2012-08-30. Global existence and decay for solutions of the Hele-Shaw flow with injection. https://arxiv.org/abs/1208.6213

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