Related papers: Exact Solutions for Modified Burgers Vortex
Blowups of vorticity for the three- and two- dimensional homogeneous Euler equations are studied. Two regimes of approaching a blowup points, respectively, with variable or fixed time are analysed. It is shown that in the $n$-dimensional…
The N-vortex solutions to the two-dimensional Ginzburg - Landau equations for the kappa=1/\sqrt(2) parameter are built. The exact solutions are derived for the vortices with large numbers of the magnetic flux quanta. The size of vortex core…
We construct splitting methods suitable for the solution of the equations of magnetohydrodynamics (MHD). Due to the physical significance of the involved operators, splittings into three or even four operators with positive coefficients are…
The dynamics of a constrained three-vortex problem, a free point vortex pair in the velocity field of a fixed point vortex, is investigated. The underlying dynamical system is simplified using a coordinate transformation and categorized…
Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations…
The evolution of a small-amplitude localized vortex disturbance in an unbounded shear flow with the linear velocity profile is investigated. Based on the exact solution of the initial problem for basic flow, a revision is made of the…
Exact time-dependent solutions of nonrelativistic noncommutative Chern - Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstrom, Rocek and von…
Steady-state perturbations to a stagnation point flow of the form ${\bf U}=(0,A'y,-A'z)$ are known which consist of a periodic array of counter-rotating vortices whose axes are parallel to the $y$-axis and which lie in the plane $z=0$. A…
In this paper, we investigate the symmetry properties of a variable coefficient nonlinear space-time fractional Burgers' equation. Fractional Lie symmetries and corresponding infinitesimal generators are obtained. With the help of the…
Eulerian local region-type vortex identification criteria, including the criterion, the criterion and the criterion et al., are widely used for vortex identification due to the simplicity in applications. However, most of these criteria are…
In this paper, we establish the existence and uniqueness of solutions to the two-dimensional Burgers equation using the framework of infinite-dimensional dynamical systems. The two-dimensional Burgers equation, which models the interplay…
We provide a constructive global existence proof for the multivariate viscous Burgers equation system defined on the whole space or on a domain isomorphic to the n-torus and with time horizon up to infinity and C^{\infty}- data (satisfying…
Exact solutions of both the Navier-Stokes and Euler equations are found on the surface of a sphere. Under the assumption of a vanishing convection term, the flow of two oppositely rotating point vortices at the poles turns out to be the…
We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…
Vortices are localized planar structures that attain topological stability and can be used to describe collective behavior in a diversity of situations of current interest in nonlinear science. In high energy physics, vortices engender…
It is pointed out that for the case of (compressible) magnetohydrodynamics (MHD) with the fields $v_y(y,t)$ and $B_x(y,t)$ one can have equations of the Burgers type which are integrable. We discuss the solutions. It turns out that the…
The dynamics of curved vortex filaments is studied analytically and numerically in the framework of a three-dimensional complex Ginzburg-Landau equation (CGLE). It is proved that a straight vortex line is unstable with respect to…
We consider the motion of a vortex in an asymptotically homogeneous condensate bounded by a solid wall where the wave function of the condensate vanishes. For a vortex parallel to the wall, the motion is essentially equivalent to that…
The vortex dynamics in mesoscopic superconducting cylinders with rectangular cross section under an axially applied magnetic field is investigated in the multivortex London regime. The rectangles considered range from a square up to an…
This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by L\'evy space-time white noise with the periodic boundary condition. We rigorously discuss the regularity…