Related papers: Dynamics of vortex cap solutions on the rotating u…
We present vortex solutions for the homogeneous two-dimensional Bose-Einstein condensate featuring dipolar atomic interactions, mapped out as a function of the dipolar interaction strength (relative to the contact interactions) and…
We investigate stability properties of a type of periodic solutions of the $N$-vortex problem on general domains $\Omega\subset \mathbb{R}^2$. The solutions in question bifurcate from rigidly rotating configurations of the whole-plane…
We investigate the existence of time-periodic vortex patch solutions, in both simply and doubly-connected cases, for the two-dimensional lake equation where the depth function of the lake is assumed to be non-degenerate and radial. The…
For the class of quasi-periodic solutions of the vortex filament equation, we study connections between the algebro-geometric data used for their explicit construction and the geometry of the evolving curves. We give a complete description…
The existence of a local curve of corotating and counter-rotating vortex pairs was proven by Hmidi and Mateu in via a desingularization of a pair of point vortices. In this paper, we construct a global continuation of these local curves.…
For any positive integer $k$, we prove the existence of nontrivial $C^k$-smooth uniformly rotating solutions to the 2D incompressible Euler equations with compact spatial support. These solutions, which can be chosen to be small…
We analyze the vortex solution space of the $(2 +1)$-dimensional nonlinear Dirac equation for bosons in a honeycomb optical lattice at length scales much larger than the lattice spacing. Dirac point relativistic covariance combined with…
We investigate the emergence of finite-amplitude non-zonal flows on the sphere $\mathbb{S}^2$ arising from stationary solutions to the 2D Euler equations. By restricting the Laplace-Beltrami eigenspace to the invariant subspace of the…
In this paper we consider steady vortex flows for the incompressible Euler equations in a planar bounded domain. By solving a variational problem for the vorticity, we construct steady double vortex patches with opposite signs concentrating…
We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state…
This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described the infinitesimal, free, undamped in-plane bending vibrations of a…
We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…
We consider the free boundary problem for a liquid drop of nearly spherical shape with capillarity, and we study the existence of nontrivial (i.e., non spherical) rotating traveling profiles bifurcating from the spherical shape, where the…
Rossby-Haurwitz (RH) waves are important explicit solutions of the incompressible Euler equation on a two-dimensional rotating sphere. In this paper, we prove the orbital stability of degree-2 RH waves, which confirms a conjecture proposed…
We show that given an initial vorticity which is bounded and $m$-fold rotationally symmetric for $m \ge 3$, there is a unique global solution to the 2D Euler equation on the whole plane. That is, in the well-known $L^1 \cap L^\infty$ theory…
Let $\mathbb{S}^N\subset\mathbb{R}^{N+1}$, $N\ge 3$, be the unit sphere, and let $S_{\Theta}\subset\mathbb{S}^N$ be a geodesic ball with geodesic radius $\Theta\in(0,\pi)$. We study the bifurcation diagram…
We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can…
Motivated by recent studies in geophysical and planetary sciences, we investigate the PDE-analytical aspects of time-averages for barotropic, inviscid flows on a fast rotating sphere $S^2$. Of particular interests are the incompressible…
We address Euler's equations for irrotational gravity waves in an infinitely deep fluid rewritten in conformal variables. Stokes waves are traveling waves with the smooth periodic profile. In agreement with the previous numerical results,…
We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The construction is performed by studying the asymptotics of…