Infinite lifetime for the starlike dynamics in Hele-Shaw cells |
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| Authors: | Bjö rn Gustafsson Dmitri Prokhorov Alexander Vasil'ev |
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| Affiliation: | Department of Mathematics, Royal Institute of Technology, Stockholm 100 44, Sweden ; Department of Mathematics and Mechanics, Saratov State University, Saratov 410012, Russia ; Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile |
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| Abstract: | One of the ``folklore" questions in the theory of free boundary problems is the lifetime of the starlike dynamics in a Hele-Shaw cell. We prove precisely that, starting with a starlike analytic phase domain  , the Hele-Shaw chain of subordinating domains  ,  , exists for an infinite time under injection at the point of starlikeness. |
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| Keywords: | Free boundary problem, Hele-Shaw flow, univalent function, starlike function, L" owner-Kufarev equation |
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