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

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.
Publication status:
Published

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Publisher copy:
10.4171/IFB/321

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
European Mathematical Society Publishing House
Journal:
INTERFACES AND FREE BOUNDARIES More from this journal
Volume:
16
Issue:
3
Pages:
297-338
Publication date:
2012-08-30
DOI:
ISSN:
1463-9963
Language:
English
Keywords:
Pubs id:
pubs:407507
UUID:
uuid:230ec71c-f428-4dcc-8b17-d57bb1c701b7
Local pid:
pubs:407507
Source identifiers:
407507
Deposit date:
2013-11-16

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