Nonstationary free boundary problem for perfect fluid with surface tension (Q1820044)

A free boundary problem for a nonstationary irrotational motion of incompressible inviscid fluid was considered as a simplified model of a flow around a celestial body. The author considered only the flow in the plane through the equator, which may be regarded as a two-dimensional one. Self-gravitation of the fluid was neglected and only the gravitation due to the inside of the equator was taken into account. The problem was formulated by the perturbation method. The author has shown that the trivial solution is stable only if a certain condition is satisfied.