相关论文: Quantitative estimates for uniformly-rotating vort…

In this paper, we prove nonlinear stability of planar vortex patches concentrated near an isolated minimum point of the Robin function in a general bounded domain. These vortex patches are stationary solutions of the two-dimensinal…

We prove persistence of the regularity of the boundary of vortex patches for a large class of transport equations in the plane. The velocity field is given by convolution of the vorticity with an odd kernel, homogeneous of degree $-1$ and…

In this paper, we investigate the existence of a finite number of vortex patches for the generalized surface quasi-geostrophic (gSQG) equations with $\alpha \in [1,2)$, focusing on configurations that may rotate uniformly, translate, or…

We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a 2D point-like model,…

We construct a series of patch type solutions for incompressible Euler equation on $\mathbb S^2$, which constitutes the regularization for steady or traveling point vortex systems. We first prove the existence of $k$-fold symmetric patch…

In this paper, we prove the existence of $m$-fold rotating patches for the Euler equations in the disc, for both simply-connected and doubly-connected cases. Compared to the planar case, the rigid boundary introduces rich dynamics for the…

We consider a "symmetric" quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of "rapid" rotation. We examine this problem using a purely numerical approach, as well as a…

We consider vortex patch solutions of the incompressible Euler equations in the plane. It is shown that the winding number around the origin for most particles in the patch grows linearly in time when the initial patch is close to a disk…

This paper concerns the study of some special ordered structures in turbulent flows. In particular, a systematic and relevant methodology is proposed to construct non trivial and non radial rotating vortices with non necessarily uniform…

In the present study, we test the predictions of the {\omega}-Equation against laboratory experiments with direct measurements of the vertical velocity w. Our results are further completed through the use of theoretical models of oceanic…

Experimental and simulational studies of the dynamics of vortex reconnections in quantum fluids showedthat the distance $d$ between the reconnecting vortices is close to a universal time dependence $d=D[\kappa|t_0-t|]^\alpha$ with $\alpha$…

We prove the persistence of boundary smoothness of vortex patches for a non-linear transport equation in $\mathbb{R}^n$ with velocity field given by convolution of the density with an odd kernel, homogeneous of degree $-(n-1)$ and of class…

The deformation of two-dimensional vortex patches in the vicinity of fluid boundaries is investigated. The presence of a boundary causes an initially circular patch of uniform vorticity to deform. Sufficiently far away from the boundary,…

The motion of incompressible and ideal fluids is studied in the plane. The stability in $L^1$ of circular vortex patches is established among the class of all bounded vortex patches of equal strength without any restriction on the size of…

We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices.…

This paper analyzes the space of steady rotating solutions to the two-dimensional incompressible Euler equations nearby vortex patch solutions satisfying a natural nondegeneracy condition. We address the question of desingularization and…

An explicit expression for the vortex velocity field as a function of the order parameter field is derived for the case of point defects in the O(n) symmetric time-dependent Ginzburg-Landau model. This expression is used to find the vortex…

The main result is that given a generic self-similarly expanding configuration of 3 point vortices that start sufficiently far out, we can instead take compactly supported vorticity functions, and the resulting solution to 2D incompressible…

In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function $q$…

We consider concentrated vorticities for the Euler equation on a smooth domain $\Omega \subset \mathbf{R}^2$ in the form of \[ \omega = \sum_{j=1}^N \omega_j \chi_{\Omega_j}, \quad |\Omega_j| = \pi r_j^2, \quad \int_{\Omega_j} \omega_j d\mu…