Hele–Shaw flows with a free boundary produced by multipoles
1993 ◽
Vol 4
(2)
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pp. 97-120
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Keyword(s):
We study Hele–Shaw flows with a moving boundary and multipole singularities. We find that such flows can be defined only on a finite time interval. Using a complex variable approach, we construct a family of explicit solutions for a single multipole. These solutions turn out to have the maximal possible lifetime in a certain class of solutions.We also discuss the generalized Hele-Shaw model in which surface tension at the moving boundary is considered, and develop a method of finding steady shapes. This method yields new one-parameter families of stationary solutions. In the Appendix we discuss a connection between these solutions and a variational problem of potential theory.
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2004 ◽
Vol 41
(2)
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pp. 570-578
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Keyword(s):
2011 ◽
Vol 34
(7)
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pp. 841-849
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Keyword(s):
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2017 ◽
Vol 354
(15)
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pp. 6747-6765
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