Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MOTION OF VORTEX FILAMENTS IN 3-MANIFOLDS

  • PAK, HEE-CHUL (Department of Applied Mathematics, Dankook University)
  • Published : 2005.02.01
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Abstract

In this paper, the visco-Da-Rios equation; (0.1) ($$\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}$$) is investigated on 3-dimensional complete orientable Riemannian manifolds. The global existence of solution is discussed by trans-forming (0.1) into a cubic nonlinear Schrodinger equation for complete orient able Riemannian 3-manifolds of constant curvature.

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