Related papers: Some exact Bradlow vortex solutions
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Spiral structure is one of the most common structures in the nature flows. A general steady spiral solution of incompressible inviscid axisymmetric flow was obtained analytically by applying separation of variables to the 3D Euler…
The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a…
We derive an exact equation of motion for a non-relativistic vortex in two- and three-dimensional models with a complex field. The velocity is given in terms of gradients of the complex field at the vortex position. We discuss the problem…
We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating…
For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the solution is regular. Roughly speaking this implies that, near…
For the $2D$ Euler equation in vorticity formulation, we construct localized smooth solutions whose critical Sobolev norms become large in a short period of time, and solutions which initially belong to $L^\infty \cap H^1$ but escapes $H^1$…
We consider relative equilibrium solutions of the two-dimensional Euler equations in which the vorticity is concentrated on a union of finite-length vortex sheets. Using methods of complex analysis, more specifically the theory of the…
We consider two types of the time-dependent Ginzburg-Landau equation in 2D bounded domains: the heat-flow equation and the Schroedinger equation. The system of ordinary differential equations is obtained that describes the evolution of the…
We study the dynamics of vortices with arbitrary topological charges in weakly interacting Bose-Einstein condensates using the Adomian Decomposition Method to solve the nonlinear Gross-Pitaevskii equation in polar coordinates. The solutions…
We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated…
Incompressible fluids on curved surfaces are considered with respect to the interplay between topology, geometry and fluid properties using a surface vorticity-stream function formulation, which is solved using parametric finite elements.…
We study isolated, stationary, axially symmetric vortex solutions in (2+1)-dimensional viscous conformal fluids. The equations describing them can be brought to the form of three coupled first order ODEs for the radial and rotational…
The general problem of a perfect incompressible fluid motion with vortex areas and variant constant vorticities is formulated. The M.A. Goldshtik's variational approach is considered on research of dual problems for flows with vortex and…
Vortex streets are periodic configurations of vortices propagating through an irrotational flow. In this paper, we study streets of hollow vortices, which are solutions to the free boundary $2$-d irrotational incompressible Euler equations.…
We explicitly derive a~vortex inspired solution for the metric perturbation within the linearized Einsteins general theory of relativity in arbitrary dimensions $D\geq 4$. We focus on $D=4$ where our solution is the gravitational analog of…
By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and…
In this paper, we prove the solvability of the vortex equation on a holomorphic vector bundle over a compact Hermitian manifold using the continuity method, and show the Kobayashi-Hitchin correspondence for holomorphic pairs. This work…
A new class of vortex solutions is found in SU(2) gauge theories with two adjoint representation Higgs bosons. Implications of these new solutions and their possible connection with Center Gauge fixed pure gauge theories are discussed.
The new type of solutions of the London equation for type-II superconductors is obtained to describe the ring-shaped (toroidal) Abrikosov vortices. The specific feature of these solutions is the self-consistent localization of both the…