Related papers: Steady vortex patches on flat torus with a constan…
In this paper, we study the uniformly rotating vortex patch solutions for the 2D incompressible Euler equations. Specifically, we prove that if the patch solution is close to the Rankine vortex in a certain weak topology, it is either the…
In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows…
Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…
For the 2D incompressible Euler equations, we establish global-in-time ($t \in \mathbb{R}$) stability of vortex quadrupoles satisfying odd symmetry with respect to both axes. Specifically, if the vorticity restricted to a quadrant is…
The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of…
In this article, we study Lions' density patch problem in two space dimensions at critical regularity. We prove global existence, uniqueness, and stability for a fluid occupying a bounded Lipschitz region surrounded by vacuum and evolving…
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…
The single vortex problem in a strongly correlated bosonic system is investigated self-consistently within the mean-field theory of the Bose-Hubbard model. Near the superfluid-Mott transition, the vortex core has a tendency toward the…
We prove a sufficient condition for nonlinear stability of relative equilibria in the planar $N$-vortex problem. This result builds on our previous work on the Hamiltonian formulation of its relative dynamics as a Lie--Poisson system. The…
Clusters of co-rotating vortices on compact fluid domains exhibit a simple collective dynamics, combining coherent global rotation with a slow breathing of the cluster size. In this work, we investigate an analytically tractable model of…
We present a combined experimental and theoretical investigation of the formation and decay kinetics of vortices in two dimensional, compressible quantum turbulence. We follow the temporal evolution of a quantum fluid of exciton polaritons,…
The discrete vortex lattices in a ferromagnet/superconductor bilayer are studied when the ferromagnet has periodic stripe domains with an out-of-plane magnetization. The vortices are assumed to be situated periodically on chains in the…
It was recently found that the Lee-Huang-Yang (LHY) correction to the mean-field Hamiltonian suppresses the collapse and creates stable localized modes (two-component "quantum droplets", QDs) in two and three dimensions. We construct…
In this paper, we investigate the asymptotic behavior of solutions to the Navier-Stokes equations in the half-plane under high Reynolds number conditions, where the initial vorticity belongs to the Yudovich class and is supported away from…
For the damped wave equation on a compact manifold with {\em continuous} dampings, the geometric control condition is necessary and sufficient for {uniform} stabilisation. In this article, on the two dimensional torus, in the special case…
We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of…
We present a general regularization procedure for piecewise smooth vector fields whose discontinuity locus is a variety of normal crossings type. We show that such regularization can be smoothed through a finite sequence of blowings-up,…
We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a…
We consider the steady Euler flows past an obstacle in an infinity long strip with horizontal constant velocity at infinity, prescribed circulation around the obstacle and sharply concentrated patch-type vorticity. The construction of these…
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying…