# Sul moto d’un liquido indefinito con un filetto vorticoso di forma qualunque

@article{RiosSulMD, title={Sul moto d’un liquido indefinito con un filetto vorticoso di forma qualunque}, author={Luigi Sante Da Rios}, journal={Rendiconti del Circolo Matematico di Palermo (1884-1940)}, volume={22}, pages={117-135} }

## 231 Citations

Higher-dimensional Hasimoto transform and Euler fluids: counterexamples and generalizations

- Physics, Mathematics
- 2019

The Hasimoto transform takes the binormal equation to the NLS and barotropic fluid equations. We show that in higher dimensions its existence would imply the conservation of the Willmore energy in…

Higher-dimensional Hasimoto transform for vortex membranes: counterexamples and generalizations

- 2019

The Hasimoto transform takes the binormal equation to the NLS and barotropic fluid equations. We show that in higher dimensions its existence would imply the conservation of the Willmore energy in…

Solutions lagrangiennes ou singulières des équations de Vlasov-Poisson et d'Euler : existence, unicité, interactions et collisions

- Physics
- 2019

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and…

Motion of a helical vortex

- Physics
- 2015

We study the motion of a single helical vortex in an unbounded, inviscid, incompressible fluid. The vortex is an infinite tube whose centerline is a helix and whose cross section is a circle of small…

Nested toroidal flux surfaces in magnetohydrostatics. Generation via soliton theory

- PhysicsJournal of Plasma Physics
- 2003

It is shown that the classical magnetohydrostatic equations of an infinitely conducting fluid reduce to the integrable potential Heisenberg spin equation subject to a Jacobian condition if the…

Travelling helices and the vortex filament conjecture in the incompressible Euler equations

- Mathematics, Physics
- 2020

We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity form. A classical question that goes back to Helmholtz is to describe the evolution of solutions with a high concentration…

Commuting Hamiltonian Flows of Curves in Real Space Forms

- Mathematics
- 2018

Starting from the vortex filament flow introduced in 1906 by Da Rios, there is a hierarchy of commuting geometric flows on space curves. The traditional approach relates those flows to the nonlinear…

Hypersurface Constrained Elasticae in Lorentzian Space Forms

- Mathematics
- 2015

We study geodesics in hypersurfaces of a Lorentzian space form , which are critical curves of the -bending energy functional, for variations constrained to lie on the hypersurface. We characterize…

Regular and Chaotic Particle Motion Near a Helical

- 2007

In this paper we analyze the ow induced by a helical vortex lament in an axisymmetric time-dependent strain eld. We rst discuss bifurcations and the structure of particle paths in the unperturbed…

Nonlinear dispersive partial differential equations of physical relevance with applications to vortex dynamics

- Physics
- 2014

Nonlinear dispersive partial differential equations occur in a variety of areas within mathematical physics and engineering. We study several classes of such equations, including scalar complex…

## References

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