Related papers: Desingularization of vortex rings in 3 dimensional…
We revisit the vortex filament conjecture for three-dimensional inviscid and incompressible Euler flows with helical symmetry and no swirl. Using gluing arguments, we provide the first construction of a smooth helical vortex filament in the…
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…
We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the…
Numerical simulation has indicated that vortex structures can exist for a long time in the form of quantized filaments on arrays of coupled weakly dissipative nonlinear oscillators in a finite three-dimensional domain under a resonant…
We study the global-in-time dynamics of vortex rings for the three-dimensional incompressible Euler equations, under the assumption of axisymmetric flows without swirl. For a broad class of initial data sharing only the macroscopic…
Two-dimensional Euler flows, in the plane or on simple surfaces, possess a material invariant, namely the scalar vorticity normal to the surface. Consequently, flows with piecewise-uniform vorticity remain that way, and moreover evolve in a…
A classical problem for the two-dimensional Euler flow for an incompressible fluid confined to a smooth domain. is that of finding regular solutions with highly concentrated vorticities around $N$ moving {\em vortices}. The formal dynamic…
The aim of this contribution is to make a connection between two recent results concerning the dynamics of vortices in incompressible planar flows. The first one is an asymptotic expansion, in the vanishing viscosity limit, of the solution…
We study the asymptotic behavior and the asymptotic stability of the two-dimensional Euler equations and of the two-dimensional linearized Euler equations close to parallel flows. We focus on spectrally stable jet profiles $U(y)$ with…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is rapidly increasing in time, the corresponding laminar profile of the…
We disclose a class of stable nonlinear traveling waves moving at specific constant velocities within symmetric two-dimensional quantum droplets. We present a comprehensive analysis of these traveling bubbles and identify three…
We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of…
The vortex dynamics of Euler's equations for a constant density fluid flow in $R^4$ is studied. Most of the paper focuses on singular Dirac delta distributions of the vorticity two-form $\omega$ in $R^4$. These distributions are supported…
Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an…
We consider a wide class of approximate models of evolution of singular distributions of vorticity in three dimensional incompressible fluids and we show that they have global smooth solutions. The proof exploits the existence of suitable…
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
Two-dimensional arrays of nonlinear electric oscillators are considered theoretically, where nearest neighbors are coupled by relatively small, constant, but non-equal capacitors. The dynamics is approximately reduced to a weakly…
In this investigation we revisit the question of the linear stability analysis of 2D steady Euler flows characterized by the presence of compact regions with constant vorticity embedded in a potential flow. We give a complete derivation of…
In this paper, we perform a careful numerical study of nearly singular solutions of the 3D incompressible Euler equations with smooth initial data. We consider the interaction of two perturbed antiparallel vortex tubes which was previously…
We consider a two-dimensional, two-layer, incompressible, steady flow, with vorticity which is constant in each layer, in an infinite channel with rigid walls. The velocity is continuous across the interface, there is no surface tension or…