Free Boundary Value Problem for the Axisymmetric Fluid’s Flow with Surface Tension and Wedging Forces

Abstract

A free boundary value problem with surface tension and wedging forces is consid-ered. From the mathematical point of view it leads to a boundary value problem in which the mean and Gauss curvatures appear in the boundary condition on the unknown surface. The variational problem is formulated and it is proved that its solution is the solution of the free boundary value problem. Infinite smoothness of the free surface is proved and it is also proved that the curve generating the free surface is analytic for some values of the problem parameters.