English
Related papers

Related papers: Full well-posedness of point vortex dynamics corre…

200 papers

In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…

Analysis of PDEs · Mathematics 2023-05-16 Guodong Wang

General properties of conservative hydrodynamic-type models are treated from positions of the canonical formalism adopted for liquid continuous media, with applications to the compressible Eulerian hydrodynamics, special- and…

Fluid Dynamics · Physics 2009-11-10 Victor P. Ruban

We derive a fully quantum-mechanical equation of motion for a vortex in a 2-dimensional Bose superfluid, in the temperature regime where the normal fluid density $\rho_n(T)$ is small. The coupling between the vortex "zero mode" and the…

Mesoscale and Nanoscale Physics · Physics 2012-05-21 L. Thompson , P. C. E. Stamp

We consider the 2D Euler equation with bounded initial vorticity and perturbed by rough transport noise. We show that there exists a unique solution, which coincides with the starting condition advected by the Lagrangian flow. Moreover, the…

Analysis of PDEs · Mathematics 2024-11-01 Leonardo Roveri , Francesco Triggiano

The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as…

Fluid Dynamics · Physics 2021-09-29 Jasmine M. Andersen , Andrew A. Voitiv , Mark E. Siemens , Mark T. Lusk

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we…

Analysis of PDEs · Mathematics 2009-11-10 Thierry Gallay , C. Eugene Wayne

We study the Euler equation on the rotating sphere in the case where the absolute vorticity is initially sharply concentrated around several points. We follow the literature already concerning vorticity confinement for the planar Euler…

Analysis of PDEs · Mathematics 2026-05-05 Martin Donati , Emeric Roulley

It is known that the quantized vortices in a superfluid can be described by a dual electromagnetic model through the duality transformation. Recently a new technique, which can selectively remove atoms from a Bose-Einstein condensate, was…

Mesoscale and Nanoscale Physics · Physics 2009-11-10 Hui Zhai , Qi Zhou

The experimental investigation of spontaneously created vortices is of utmost importance for the understanding of quantum phase transitions towards a superfluid phase, especially for two dimensional systems that are expected to be governed…

We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…

Mathematical Physics · Physics 2020-10-21 Matthew Rosenzweig

Optical vortices arise as phase singularities of the light fields and are of central interest in modern optical physics. In this paper, some existence theorems are established for stationary vortex wave solutions of a general class of…

Mathematical Physics · Physics 2012-09-24 Yisong Yang , Ruifeng Zhang

We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…

Analysis of PDEs · Mathematics 2019-04-15 Olivier Glass , Christophe Lacave , Alexandre Munnier , Franck Sueur

The study of the 2D Euler equation with non Lipschitzian velocity was initiated by Yudovich in [19] where a result of global well-posedness for essentially bounded vorticity is proved. A lot of works have been since dedicated to the…

Analysis of PDEs · Mathematics 2012-04-27 Frederic Bernicot , Sahbi Keraani

We develop the kinetic theory of point vortices in two-dimensional hydrodynamics and illustrate the main results of the theory with numerical simulations. We first consider the evolution of the system "as a whole" and show that the…

Statistical Mechanics · Physics 2009-11-13 P. H. Chavanis , M. Lemou

We introduce a local-in-time existence and uniqueness class for solutions to the 2d Euler equation with unbounded vorticity. Furthermore, we show that solutions belonging to this class can develop stronger singularities in finite time,…

Analysis of PDEs · Mathematics 2024-01-01 Tarek M. Elgindi , Ryan W. Murray , Ayman R. Said

In non-hermitian systems, the particular position at which two eigenstates coalesce under a variation of a parameter in the complex plane is called an exceptional point. A non-perturbative theory is proposed which describes the evolution of…

The problem of a periodic scalar field on a two-dimensional dynamical random lattice is studied with the inclusion of vortices in the action. Using a random matrix formulation, in the continuum limit for genus zero surfaces the partition…

High Energy Physics - Theory · Physics 2011-07-19 S. Dalley

We report results of systematic investigation of dynamics featured by moving two-dimensional (2D) solitons generated by the fractional nonlinear Schroedinger equation (FNLSE) with the cubic-quintic nonlinearity. The motion of solitons is a…

Pattern Formation and Solitons · Physics 2024-02-28 Thawatchai Mayteevarunyoo , Boris A. Malomed

Vortex lattices -- highly ordered arrays of vortices -- are known to arise in quantum systems such as type II superconductors and Bose-Einstein condensates. More recently, similar arrangements have been reported in classical rotating…

Fluid Dynamics · Physics 2025-10-09 Julián Amette Estrada , Alexandros Alexakis , Marc E. Brachet , Pablo D. Mininni

The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the…

Fluid Dynamics · Physics 2014-09-19 Florin Spineanu , Madalina Vlad