MOTION OF VORTEX FILAMENTS IN 3-MANIFOLDS

Title & Authors
MOTION OF VORTEX FILAMENTS IN 3-MANIFOLDS
PAK, HEE-CHUL;

Abstract
In this paper, the visco-Da-Rios equation; (0.1) ($\small{\frac{{\partial}{\gamma}}{{\partial}t}=\frac{{\partial}{\gamma}}{{\partial}s}{\bigwedge}\frac{D}{ds}\frac{{\partial}{\gamma}}{{\partial}s}+{\nu}\frac{{\partial}{\gamma}}{{\partial}s}}$) 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;
Language
English
Cited by
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