Article Contents
Article Contents

# Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension

• Travelling wave solutions of a two-dimensional gaseous star with self-gravity and surface tension are considered. The star rotates along a clockwise direction with a travelling speed. The governing equations on a whole unknown domain are changed to ones on the boundary using the Dirichlet-Neumann operator. The problem of the existence of its periodic solutions is equivalent to one of a functional equation. After applying the method of Lyapunov-Schmidt reduction, the reduced equation of this functional equation has a generalized Pitchfork bifurcation with the bifurcation parameter being the travelling speed. This shows that there exist two nontrivial periodic solutions.
Mathematics Subject Classification: Primary: 35B10, 35B32; Secondary: 76B15.

 Citation:

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