On zonal steady solutions to the 2D Euler equations on the rotating unit sphere

Abstract The present paper studies the structure of set stationary solutions to incompressible Euler equations on rotating unit sphere that are near two basic zonal flows: Rossby–Haurwitz solution degree 2 and rigid rotation Y 1 0 along polar axis. We construct a new family non-zonal steady arbitrarily close in analytic regularity second stream function, for any given sphere. This shows non-linear inviscid damping flow cannot be expected this solution. On other hand, we prove that, under suitable conditions sphere, enough must itself zonal, witnessing some sort rigidity inherited from equation, geometry base flow. Nevertheless, when fail, is much richer able existence both explicit travelling wave bifurcating , same spirit as those emanating 2.