A priori estimates for fluid Interface problems
classification
🧮 math.AP
math.DG
keywords
estimatesinterfacefrac32kcalculationconsequenceconsiderconsiderationscurvature
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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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