广义表面准地转方程光滑行进的圆形涡对的 存在性与稳定性

Smooth traveling-wave solutions to the inviscid surface quasi-geostrophic equations

In a recent article by Gravejat and Smets, it is built smooth solutions to the inviscid surface quasi-geostrophic equation that have the form of a traveling wave. In this article we work back on their construction to provide solution to a more general class of quasi-geostrophic equation where the half-laplacian is replaced by any fractional laplacian.

一般表面准地转方程中慢行波解的研究

Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation

本文研究了广义表面准地转方程中慢传播行波解的存在性与稳定性，并通过变分方法和集中-紧致原理建立了相关稳定性定理。

Existence and Stability of the Lamb Dipoles for the Quasi-Geostrophic Shallow-Water Equations

In this paper, we prove the nonlinear orbital stability of vortex dipoles for the quasi-geostrophic shallow-water (QGSW) equations. The vortex dipoles are explicit travelling wave solutions to the QGSW equations, which are analogues of the classical circular vortex of Lamb and Chaplygin for the steady planar Euler equations. We establish a variational characterization of these vortex poles, which provides a basis for the stability result.

云层尺度行星大气中zonal带中大气行波的分类

Classification of atmospheric traveling waves at cloud level

本文对云层尺度行星大气中zonal带中的行波进行了分类，揭示了其动态可能性及内在约束。

Imperfect bifurcation for the quasi-geostrophic shallow-water equations

We study analytical and numerical aspects of the bifurcation diagram of simply-connected rotating vortex patch equilibria for the quasi-geostrophic shallow-water (QGSW) equations. The QGSW equations are a generalisation of the Euler equations and contain an additional parameter, the Rossby deformation length $\EE^{-1}$, which enters in the relation between streamfunction and (potential) vorticity. The Euler equations are recovered in the limit $\EE\to 0$. We prove, close to circular (Rankine) vortices, the persistence of the bifurcation diagram for arbitrary Rossby deformation length. However …

Global solutions for the generalized SQG equation and rearrangements

In this paper, we study the existence of rotating and traveling-wave solutions for the generalized surface quasi-geostrophic (gSQG) equation. The solutions are obtained by maximization of the energy over the set of rearrangements of a fixed function. The rotating solutions take the form of co-rotating vortices with $N$-fold symmetry. The traveling-wave solutions take the form of translating vortex pairs. Moreover, these solutions constitute the desingularization of co-rotating $N$ point vortices and counter-rotating pairs. Some other quantitative properties are also established.