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Motion of vortex filaments in 3-manifolds
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Abstract
In this paper, the visco-Da-Rios equation;begin{align}frac{partial gamma }{partial t} = frac{partial gamma }{partial s}wedge frac{D}{d s} frac{partial gamma }{partial s}+ nu frac{partial gamma }{partial s}label{LIE}end{align}is investigatedon 3-dimensional complete orientable Riemannian manifolds.The global existence of solution is discussed by transforming(ref{LIE}) into a cubic nonlinear Schr"{o}dinger equationfor complete orientable Riemannian 3-manifoldsof constant curvature.
참고문헌 (6)
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- "Flow via binormal in 3-manifolds"
- "Geometric Realizations ofFordy-Kulish nonlinear Schr"odinger systems, Pacific", pp.157~ (2000)
- "A Comprehensive Introduction to RiemannianGeometry Publish or Perish", 2 (1979), Inc.
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