Stability of Hill's spherical vortex

Filamentation near Hill's vortex

For the axisymmetric incompressible Euler equations, we prove linear in time filamentation near Hill's vortex: there exists an arbitrary small outward perturbation growing linearly for all times. This is based on combining the recent nonlinear orbital stability obtained in [13] with a dynamical bootstrapping scheme for particle trajectories. These results rigorously confirm numerical simulations by Pozrikidis [45] in 1986.

反向传播的Hill球形涡对的稳定性

Stability of oppositely-propagating pair of Hill's spherical vortices

该研究在三维不可压缩轴对称Euler方程下证明了反向传播Hill球形涡对的稳定性，通过分析相互作用能与能量最大化序列紧性结合的方法，得到涡剖面始终接近Hill涡的结论，并给出最优传播速度估计。

Hill--Norbury 族附近的光滑且旋转的稳态涡环

Smooth and swirling steady vortex rings near the Hill--Norbury family

本文研究三维欧拉方程中 Hill--Norbury 涡环族的去奇异化，证明小通量成员是无限阶光滑行波解的极限，并首次验证该族在光滑涡环中不孤立。

Ginzburg-Landau patterns in circular and spherical geometries: vortices, spirals and attractors

This paper consists of three results on pattern formation of Ginzburg-Landau $m$-armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely describe the global bifurcation diagram of vortex equilibria. Second, we prove persistence of all bifurcation curves under perturbations of parameters, which yields the existence of spiral waves for the complex Ginzburg-Landau equation. Third, we explicitly construct the global attractor of $m$-armed vortex solutions. Our main tool is a new shooting method that allows us to prove hyperbolicity of vortex equilibria in…

无粘流体中的稳态气泡与液滴

Steady bubbles and drops in inviscid fluids

本文通过微扰方法结合隐函数定理与分岔分析，构造了带表面张力的两相 Euler 方程的稳态非球形行波解，证明了表面张力模型比单相 Euler 方程具有更丰富的解结构。

Higher Dimensional Vortex Standing Waves for Nonlinear Schr{ö}dinger Equations

We study standing wave solutions to nonlinear Schr{ö}dinger equations, on a manifold with a rotational symmetry, which transform in a natural fashion under the group of rotations. We call these vortex solutions. They are higher dimensional versions of vortex standing waves that have been studied on the Euclidean plane. We focus on two types of vortex solutions, which we call spherical vortices and axial vortices.