6 papers
On Arnold-type stability theorems for the Euler equation on a sphere
Daomin Cao, Guodong Wang
In this paper, we establish three Arnold-type stability theorems for steady or rotating solutions of the incompressible Euler equation on a sphere. Specifically, we prove that if t…
Quantitative Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus
Fatao Wang, Guodong Wang, Xiaoxue Zhu
In this paper, we establish quantitative estimates for the orbital stability of the first Laplacian eigenstates of the incompressible Euler equation on a two-dimensional flat torus…
Orbital Stability of First Laplacian Eigenstates for the Incompressible Euler Equation on a Flat 2-Torus
Guodong Wang
On a two-dimensional flat torus, Laplacian eigenfunctions admit explicit trigonometric representations. It is known that every first eigenstate on a rectangular or square torus is…
Stability of a class of exact solutions of the incompressible Euler equation in a disk
Guodong Wang
We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Eul…
Nonlinear stability of plane ideal flows in a periodic channel
Guodong Wang
In this paper, we establish two stability theorems for steady or traveling solutions of the two-dimensional incompressible Euler equation in a finite periodic channel, extending Ar…
Desingularization of vortices for the incompressible Euler equation on a sphere
Daomin Cao, Shuanglong Li, Guodong Wang
In this paper, we construct a family of global solutions to the incompressible Euler equation on a standard 2-sphere. These solutions are odd-symmetric with respect to the equatori…