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Stability and bifurcation of a rotating planar liquid drop. (English) Zbl 0651.76021
Summary: The stability and symmetry breaking bifurcation of a planar liquid drop is studied using the energy-Casimir method and singularity theory. It is shown that a rigidly rotating circular drop of radius r with surface tension coefficient \(\tau\) and angular velocity \(\Omega\) /2 is stable if (\(\Omega\) /2) \(2<3\tau /r\) 3. A new branch of stable rigidly rotating relative equilibria invariant under rotation through \(\pi\) and reflection across two axes bifurcates from the branch of circular solutions when (\(\Omega\) /2) \(2=3\tau /r\) 3.

MSC:
76E30 Nonlinear effects in hydrodynamic stability
76T99 Multiphase and multicomponent flows
76U05 General theory of rotating fluids
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