On the Young-Laplace relation and the evolution of a perturbed ellipsoid

Author:
George Dassios

Journal:
Quart. Appl. Math. **72** (2014), 21-32

MSC (2010):
Primary 35B35, 35Q35, 35J25

DOI:
https://doi.org/10.1090/S0033-569X-2013-01321-7

Published electronically:
November 20, 2013

MathSciNet review:
3185130

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Abstract: The Young-Laplace relation states that the interface separating two fluids, develops in such a way that the difference between the outer and the inner pressure remains proportional to the mean curvature at every point of the interface. This relation guides the evolution of a free boundary. Considering the importance of the ellipsoidal surfaces as free boundaries in anisotropic evolutions, it is of great interest to have ready-to-use formulae for the mean curvature of a perturbed ellipsoidal surface. These formulae provide the basis for the stability analysis of free boundary value problems in Fluid Mechanics. The present work calculates the first order approximation of the local curvatures for a surface which is a perturbation of an ellipsoid.

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Additional Information

**George Dassios**

Affiliation:
Department of Chemical Engineering, University of Patras and ICE-HT/FORTH, Patras, Greece

DOI:
https://doi.org/10.1090/S0033-569X-2013-01321-7

Received by editor(s):
February 22, 2012

Published electronically:
November 20, 2013

Article copyright:
© Copyright 2013
Brown University