11 papers
Lyapunov Unstable Motion Bifurcating from a Circular Vortex Filament
Masashi Aiki, Mitsuo Higaki
This paper investigates the dynamics of closed vortex filaments in governed by the Localized Induction Equation. Recently, Aiki and Higaki (2026) established the nonlinear o…
Stability of the Shape for Circular Vortex Filaments under Non-Symmetric Perturbations
Masashi Aiki, Mitsuo Higaki
We establish the nonlinear orbital stability of circular vortex filaments governed by the Localized Induction Equation (LIE) under non-symmetric perturbations, within the framework…
Long-time behavior of an Arc-shaped Vortex Filament and its Application to the Stability of a Circular Vortex Filament
Masashi Aiki
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We s…
The Hasimoto Transformation for a Finite Length Vortex Filament and its Application
Masashi Aiki
We consider two nonlinear equations, the Localized Induction Equation and the cubic nonlinear Schrödinger Equation, and prove that the solvability of certain initial-boundary value…
Head-On Collision of a Pair of Coaxial Circular Vortex Filament
Masashi Aiki
We consider the head-on collision of two coaxial vortex rings described as the motion of two circular vortex filaments under the localized induction approximation. We prove the exi…
On the Existence of Leapfrogging Pair of Circular Vortex Filaments
Masashi Aiki
We propose and analyze a system of nonlinear partial differential equations describing the motion of a pair of vortex filaments. Furthermore, for a pair of coaxial circular vortex…
Motion of a Vortex Filament on a Slanted Plane
Masashi Aiki
We consider a nonlinear model equation, known as the Localized Induction Equation, describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. We p…
Motion of a Vortex Filament in an External Flow
Masashi Aiki, Tatsuo Iguchi
We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take int…
Motion of a Vortex Filament with Axial Flow in the Half Space
Masashi Aiki, Tatsuo Iguchi
We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensiona…
Solvability of an Initial-Boundary Value Problem for a Second Order Parabolic System with a Third Order Dispersion Term
Masashi Aiki, Tatsuo Iguchi
We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion…
Motion of a Vortex Filament in the Half Space
Masashi Aiki, Tatsuo Iguchi
A model equation for the motion of a vortex filament immersed in three dimensional, incompressible and inviscid fluid is investigated as a humble attempt to model the motion of a t…