Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials
Keyword(s):
We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.
2000 ◽
Vol 128
(12)
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pp. 3483-3492
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2004 ◽
pp. 549-576
1994 ◽
Vol 261
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pp. 199-222
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2000 ◽
Vol 61
(1)
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pp. 216-244
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2003 ◽
Vol 3
(4)
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pp. 549-576
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1992 ◽
Vol 22
(2)
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pp. 237-257
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1984 ◽
Vol 14
(2)
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pp. 265-281
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Keyword(s):