The stability of a fluid cylinder in a plane-parallel flow of an ideal fluid

The plane problem of a steady-state potential flow of an ideal fluid around an infinite fluid cylinder with surface tension is considered. A family of solutions is constructed. An approximate relation is found between the Weber number and the ratio of the sizes of the cross-sections of the cylinder along the normal and along the free stream velocity. (A ratio of 11/2 corresponds to the exact McLeod special solution.) The problem of the stability of this flow is solved in the sense of a relaxed Lyapunov definition. For a ratio of the density of the cylinder to the density of the fluid flowing around it of less than 26.35, the flow is stable, and, for a greater value, it is unstable. The conventional Lyapunov stability is proved when the ratio of the densities is less than 11.07.