Existence results for Hele-Shaw flow driven by surface tension

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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.
Originele taal-2Engels
Pagina's (van-tot)195-221
Aantal pagina's27
TijdschriftEuropean Journal of Applied Mathematics
Nummer van het tijdschrift2
StatusGepubliceerd - 1998

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