Global existence and decay for solutions of the Hele-Shaw flow with injection
Analysis of PDEs
2012-08-31 v1
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.
Keywords
Cite
@article{arxiv.1208.6213,
title = {Global existence and decay for solutions of the Hele-Shaw flow with injection},
author = {C. H. Arthur Cheng and Daniel Coutand and Steve Shkoller},
journal= {arXiv preprint arXiv:1208.6213},
year = {2012}
}
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25 Pages