A priori estimates for fluid Interface problems
Jalal Shatah, Chongchun Zeng
Abstract
We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in H32k +1 and the velocity fields in H32k. These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.
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