Nonbranching weak and starshaped strong solutions for Hele-Shaw dynamics |
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| Authors: | Björn Gustafsson Alexander Vasil’ev |
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| Institution: | (1) Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden;(2) Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway |
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| Abstract: | We consider multidimensional weak and strong Hele-Shaw dynamics  (t) of an advancing/receding viscous fluid injected/removed through a single finite point into/from a bounded domain (0). A class of weak solutions is shown to preserve local uniqueness in both directions. Then we also consider strong solutions (t), and show that if (0) is starshaped with respect to a small ball centered on the point of injection, then the evolution (t) exists for all time.Received: 5 March 2004 |
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| Keywords: | Primary 76D27 31B05 Secondary 76S05 35Q35 |
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