# Asymptotic integration of the equation of equilibrium for a fluid with surface tension in a gravitational field

- Authors
- Journal
- USSR Computational Mathematics and Mathematical Physics 0041-5553
- Publisher
- Elsevier
- Publication Date
- Volume
- 6
- Issue
- 6
- Identifiers
- DOI: 10.1016/0041-5553(66)90178-9

## Abstract

Abstract BOUNDARY layer methods have been used in a number of recent papers [1] for solving problems on the equilibrium and motion of a fluid with surface tension in a strong gravitational field (more precisely, with large Bond numbers). The present note proves the suitability of the method for Investigating the equilibrium of a fluid with surface tension, enclosed in a cylindrical vessel of arbitrary cross-section, in a gravitational field. Mathematically, the problem amounts to solving asymptotically an equation with a small parameter in a quasilinear elliptic operator under nonlinear boundary conditions. The method of obtaining the asymptotic solution is similar to that developed in [2, 3], while the proof of it follows the lines of [4].

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