A priori estimates for fluid Interface problems

Details A priori estimates for fluid Interface problems A priori estimates for fluid Interface problems

2006-09-20

arxiv.org/abs/math/0609542v2

Mathematics

Analysis of PDEs

17 pages, submitted, added references

Scientific paper

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 $H^{\frac32k +1}$ and the velocity fields in $H^{\frac32k}$. 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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