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A priori estimates for fluid interface problems
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DOI：10.1002/cpa.20241.png)
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Abstract
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We consider the regularity of an interface between two incompressible and inviscid fluid flows in the presence of surface tension. We obtain local-in-time estimates on the interface in H(3/2)k+1 and the velocity fields in H-(3/2)k. These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation. (c) 2007 Wiley Periodicals, Inc.
Keywords:
WATER-WAVE PROBLEM
WELL-POSEDNESS
VORTEX SHEETS
SURFACE-TENSION
SOBOLEV SPACES
MOTION
EXISTENCE
EQUATIONS
BOUNDARY
3-D
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