On the Singular Behaviour of Fluid in a Vertical Wedge

Abstract

Solutions of capillary surface equation over domains with corners are considered. It is assumed that the corner is bounded by curves which make an interior angle $2\alpha$ with $0<2\alpha <\pi$ and $\alpha +\gamma <\pi /2$, where $\gamma ,0<\gamma >\pi /2$ is the contact angle between the surface and the container wall. An asymptotic formula for the solutions near the corner is given.