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math.AP2022★ 2 cited
Uniqueness and stability of steady vortex rings for 3D incompressible Euler equation
Daomin Cao, Shanfa Lai, Guolin Qin +2
In this paper, we are concerned with the uniqueness and nonlinear stability of vortex rings for the 3D Euler equation. By utilizing Arnold 's variational principle for steady state…
math.AP2022
Existence and Stability of the Lamb Dipoles for the Quasi-Geostrophic Shallow-Water Equations
Shanfa Lai, Guolin Qin, Weicheng Zhan
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…
math.AP2022
Traveling vortex pairs for 2D Boussinesq equations
Daomin Cao, Shanfa Lai, Guolin qin
In this paper, we study the existence and asymptotic properties of the traveling vortex pairs for the two-dimensional inviscid incompressible Boussinesq equations. We construct a f…