Existence results for Hele-Shaw flow driven by surface tension

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Abstract

This paper addresses short-time existence and uniqueness of a solution to the N-dimensional Hele–Shaw flow problem with surface tension as driving mechanism. Global existence in time and exponential decay of the solution near equilibrium are also proved. The results are obtained in Sobolev spaces Hs with sufficiently large s. The main tools are perturbations of a fixed reference domain, linearization with respect to these perturbations, a quasilinearization argument based on a geometric invariance property, and a priori energy estimates.
Original languageEnglish
Pages (from-to)195-221
Number of pages27
JournalEuropean Journal of Applied Mathematics
Volume9
Issue number2
DOIs
Publication statusPublished - 1998

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