Bulletin of the Korean Mathematical Society ( Vol.42 NO.1 / 2005 ) Title Motion of vortex filaments in 3-manifolds(eng) Author Hee Chul Pak MSC 58J72, 22E30, 76B03, 35Q55 Publication Page 75-85 Page Abstract 1. Introduction 2. Hasimoto transform on Riemannian manifolds 3. The visco-Da-Rios equation and NLS-equation Own Status Keyword nonlinear Schr\"{o}dinger equation, Da-Rios equation, incompressible fluid, Hasimoto transform, Schr\"{o}dinger maps Note Summary In this paper, the visco-Da-Rios equation; egin{align} frac{partial gamma }{partial t} = frac{partial gamma }{partial s} wedge frac{D}{d s} frac{partial gamma }{partial s} + u frac{partial gamma }{partial s} label{LIE} end{align} is investigated on 3-dimensional complete orientable Riemannian manifolds. The {it global existence} of solution is discussed by transforming ( ef{LIE}) into a cubic nonlinear Schr"{o}dinger equation for complete orientable Riemannian 3-manifolds of constant curvature. Attach DVI  PDF