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math.AP2024
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…
math.AP2024
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…
math.AP2024
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…