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http://dx.doi.org/10.4134/BKMS.2005.42.1.075

MOTION OF VORTEX FILAMENTS IN 3-MANIFOLDS  

PAK, HEE-CHUL (Department of Applied Mathematics, Dankook University)
Publication Information
Bulletin of the Korean Mathematical Society / v.42, no.1, 2005 , pp. 75-85 More about this Journal
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.
Keywords
nonlinear Schrodinger equation; Da-Rios equation; incompressible fluid; Hasimoto transform; Schrodinger maps;
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