Solvability of equations for motion of a vortex filament with or without axial flow

DOI10.2977/prims/1195145146zbMath0905.35070OpenAlexW1985152651MaRDI QIDQ1387733

Atusi Tani, Takahiro Nishiyama

Publication date: 8 June 1998

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195145146

zbMATH Keywords

a priori estimatesCauchy problemunique solvabilityparabolic regularizationlocalized induction equationspatially periodic casevanishing axial flow

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Vortex flows for incompressible inviscid fluids (76B47)

Related Items (15)

On the motion of a vortex filament in an external flow according to the localized induction approximation ⋮ Geometric Schrödinger-Airy flows on Kähler manifolds ⋮ Numerical Integration of Schrödinger Maps via the Hasimoto Transform ⋮ Stability of the self-similar dynamics of a vortex filament ⋮ On the initial-boundary value problem for a vortex filament in an external flow under the localized induction approximation ⋮ On asymptotic behavior of solutions to Korteweg-de Vries type equations related to vortex filament with axial flow ⋮ New geometric flows on Riemannian manifolds and applications to Schrödinger-Airy flows ⋮ A third-order dispersive flow for closed curves into Kähler manifolds ⋮ Quasi‐Classical Approximation in Vortex Filament Dynamics. Integrable Systems, Gradient Catastrophe, and Flutter ⋮ A Remark on the Global Existence of a Third Order Dispersive Flow into Locally Hermitian Symmetric Spaces ⋮ A fifth-order dispersive partial differential equation for curve flow on the sphere ⋮ 1-D cubic NLS with several Dirac masses as initial data and consequences ⋮ KdV GEOMETRIC FLOWS ON KÄHLER MANIFOLDS ⋮ A third order dispersive flow for closed curves into almost Hermitian manifolds ⋮ Local existence of a fourth-order dispersive curve flow on locally Hermitian symmetric spaces and its application

Cites Work

• On the Cauchy problem for a coupled system of third-order nonlinear Schrödinger equations
• Solvability of the localized induction equation for vortex motion
• On the continuous limit for a system of classical spins
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• Initial and Initial-Boundary Value Problems for a Vortex Filament with or without Axial Flow
• A soliton on a vortex filament
• Exact envelope-soliton solutions of a nonlinear wave equation
• Three-dimensional distortions of a vortex filament with axial velocity
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