For small angular momentum, there exists a unique rotation orbit of smooth rotating capillary drop solutions near the circle, built by a variational bifurcation argument from a multiple eigenvalue.
Steady vortex sheets in presence of surface tension
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abstract
We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near the circular distribution for a model of two irrotational fluids with same density taking into account surface tension effects. As bifurcation parameters, we play with either the speed of rotation, the surface tension coefficient or the mean vorticity.
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Two-dimensional capillary liquid drop: Craig-Sulem formulation on $\mathbb{T}^1$ and bifurcations from multiple eigenvalues of rotating waves
For small angular momentum, there exists a unique rotation orbit of smooth rotating capillary drop solutions near the circle, built by a variational bifurcation argument from a multiple eigenvalue.