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

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