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We study the evolution of a concentrated vortex advected by a smooth, divergence-free velocity field in two space dimensions. In the idealized situation where the initial vorticity is a Dirac mass, we compute an approximation of the…
In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying its…
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 asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector)…
In this paper we construct a family of steady symmetric vortex patches for the incompressible Euler equations in an open disk. The result is obtained by studying a variational problem in which the kinetic energy of the fluid is maximized…
We investigate the rotation of a vortex around a circular obstacle in dry active matter in the presence of M half-circles distributed around the obstacle. To quantify this effect, we define the parameter {\Pi}M , which is the ratio between…
We discover the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. Such solitons can feature strongly noncanonical profiles, and we found that their properties are…
We investigate the existence of solitary gravity waves traversing a two-dimensional body of water that is bounded below by a flat impenetrable ocean bed and above by a free surface of constant pressure. Our main interest is constructing…
Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main…
The fluid dynamics video shows rigid, spatially asymmetric bodies interacting with oscillating background flows. A free rigid object, here a hollow "pyramid," can hover quite stably against gravity in the oscillating airflow with a zero…
We establish vortex dynamics for the time-dependent Ginzburg-Landau equation for asymptotically large numbers of vortices for the problem without a gauge field and either Dirichlet or Neumann boundary conditions. As our main tool, we…
This article presents a comprehensive analysis of the formation and dissipation of vortices within chaotic fluid flows, leveraging the framework of Sobolev and Besov spaces on Riemannian manifolds. Building upon the Navier-Stokes equations,…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
Vortex lattices are constructed in terms of linear combinations of solutions for Scr\"{o}dinger equation with a constant potential. The vortex lattices are mapped on the spaces with two-dimensional rotationally symmetric potentials by using…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
In view of the observed flat rotation curves of spiral galaxies and motivated by the simple fact that within newtonian gravity a stationary axisymmetric mass distribution or dark matter vortex of finite extent readily displays a somewhat…
We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of…
With increasing applied current we show that the moving vortex lattice changes its structure from a triangular one to a set of parallel vortex rows in a pinning free superconductor. This effect originates from the change of the shape of the…
We get point vortices dynamics equations on a rotating sphere surface directly from the hydrodynamic equations as representing their weak exact solution contrary to the conventional case of the use of a kinematic relationship between a…
A novel method is proposed to identify vortex boundary and center of rotation based on tubular surfaces of constant stagnation pressure and minimum of the stagnation pressure gradient. The method is derived from Crocco's theorem, which…