Related papers: Relative Equilibria of the $(1+N)$-Vortex Problem
In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with…
(abridged) We study the nonlinear evolution of the Rossby wave instability in thin disks using global 2D hydrodynamic simulations. The key questions we are addressing in this paper are: (1) What happens when the instability becomes…
We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but \textit{fixed} $\varepsilon > 0.$ The vortices of these solutions follow periodic orbits to the point vortex system of…
We study the role of the unstable equilibrium points in the transfer of matter in a galaxy using the potential of a rotating triaxial system. In particular, we study the neighbourhood of these points for energy levels and for main model…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
In this paper, we investigate steady Euler flows in a two-dimensional bounded domain. By an adaption of the vorticity method, we prove that for any nonconstant harmonic function $q$, which corresponds to a nontrivial irrotational flow,…
Three-dimensional, Gross-Pitaevskii equation (GPE) simulations are presented of the interaction between neutron superfluid vortices and proton superconductor flux tubes in a rotating, harmonic trap, representing an idealised model of the…
The paper investigates possibility of equilibrium solid-body rotation of a vortex bundle diverging at some height from a cylinder axis and terminating on a lateral wall of a container. Such a bundle arises when vorticity expands up from a…
Nonlinear evolution of a continuous spectrum of unstable waves near the first bifurcation point in circular Couette flow has been investigated. The disturbance is represented by a Fourier integral over all possible axial wavenumbers, and an…
We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium…
This paper continues a numerical investigation of orbits evolved in `frozen,' time-independent N-body realisations of smooth time-independent density distributions corresponding to both integrable and nonintegrable potentials, allowing for…
On a star graph made of $N \geq 3$ halflines (edges) we consider a Schr\"odinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there…
Bearing in mind the application to the theory of core-collapse supernovae, we performed a global linear analysis on the stability of spherically symmetric accretion flows through a standing shock wave onto a proto neutron star. As…
In this paper, we deal with the boundary value problem $-\Delta u= |u|^{4/(n-2)}u/[\ln (e+|u|)]^\varepsilon$ in a bounded smooth domain $\Omega$ in $\mathbb{R}^n$, $n\geq 3$ with homogenous Dirichlet boundary condition. Here…
The stability of the dynamical trajectories of softened spherical gravitational systems is examined, both in the case of the full $N$-body problem and that of trajectories moving in the gravitational field of non-interacting background…
In two-dimensional (2D) inviscid incompressible flow, low background vorticity distribution accelerates intense vortices (clumps) to merge each other and to array in the symmetric pattern which is called ``vortex crystals''; they are…
This article studies the vortex-wave system for the Surface Quasi-Geostrophic equation with parameter 0 < s < 1. We obtained local existence of classical solutions in H^4 under the standard ''plateau hypothesis'', H^2-stability of the…
Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations.…
The dynamics of ultralight dark matter with non-negligible self-interactions are determined by a nonlinear Schr\"odinger equation rather than by the Vlasov equation of collisionless particles. This leads to wave-like effects, such as…
The rotating neutron superfluid in the inner crust of a neutron star is threaded by quantized vortex lines. The pinning force from lattice nuclei and the Magnus force from neutron superfluid act onto a vortex line that has a finite tension.…