The Non-zonal Rossby–Haurwitz Solutions of the 2D Euler Equations on a Rotating Ellipsoid

In this article, we investigate the incompressible 2D Euler equations on a rotating biaxial ellipsoid, which model the dynamics of the atmosphere of a Jovian planet. We study the non-zonal Rossby–Haurwitz solutions of the Euler equations on an ellipsoid, while previous works only considered the case of a sphere. Our main results include: the existence and uniqueness of the stationary Rossby–Haurwitz solutions; the construction of the traveling-wave solutions; and the demonstration of the Lyapunov instability of both the stationary and the traveling-wave solutions.