相关论文: Stability of Two-dimensional Potential Flows Using…

In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…

A compactness framework is formulated for the incompressible limit of approximate solutions with weak uniform bounds with respect to the adiabatic exponent for the steady Euler equations for compressible fluids in any dimension. One of our…

The aim of these notes is to present in a comprehensive and relatively self-contained way some recent developments in the mathematical analysis of two-dimensional viscous flows. We consider the incompressible Navier-Stokes equations in the…

Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the…

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B --> 2B and A+B --> 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider…

The dynamics and statistical properties of two-dimensional (2D) turbulence are often investigated through numerical simulations of incompressible, viscous fluids in doubly periodic domains. A key challenge in 2D turbulence research is…

We construct and analyse two-dimensional, current-carrying ring solutions, known as kinky vortons, in the $\mathbb{Z}_2$-symmetric global two-Higgs-doublet model (2HDM). We demonstrate the existence of multiple dynamically stable…

At present in the fluid mechanics, mostly one like to use the vortex as a basic physical quantity, such that some exact solutions is based on the vorticity evolution equation. For the vortex flow problem with axisymmetry, it is well known…

In the present paper, recent experimental results on large scale coherent steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited from a statistical mechanics perspective. The latter is rooted on two levels of…

We study the passive particle transport generated by a circular vortex path in a 2D ideal flow confined in a circular domain. Taking the strength and angular velocity of the vortex path as main parameters, the bifurcation scheme of relative…

A new analysis of basic Couette flow, is based on an Action Principle for compressible fluids, with a Hamiltonian as well as a kinetic potential. An effective criterion for stability recognizes the tensile strength of water. This…

It is well-known that the dynamics of vortices in an ideal incompressible two-dimensional fluid contained in a bounded not necessarily simply connected smooth domain is described by the Kirchhoff--Routh point vortex system. In this paper,…

We consider the evolution of two-dimensional incompressible flows with variable density, only bounded and bounded away from zero. Assuming that the initial velocity belongs to a suitable critical subspace of L^2 , we prove a global-in-time…

The integrals of motion for a cylindrically symmetric stationary vortex are obtained in a covariant description of a mixture of interacting superconductors, superfluids and normal fluids. The relevant integrated stress-energy coefficients…

The notion of instability of a turbulent flow is introduced in the case of a von K\'arm\'an flow thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations, combined with projection onto suitable Beltrami modes.…

Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the most challenging problems in physics. Two-dimensional, fully developed turbulence may possess the largest possible symmetry, the conformal symmetry. We focus on…

Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the…

In the present study we investigate analytically the process of velocity and energy relaxation in two-phase flows. We begin our exposition by considering the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This model…

This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…

We numerically investigate the flow structure of periodic steady water waves of fixed relative mass flux propagating on rotational flows with piece-wise constant vorticity. We show that for wave solutions along the global bifurcation…