The stability of rotating vortex patches

In this paper we examine the nonlinear and linear stability of variousrotating vortex patches. These patches include the Kirchhoff ellipse, the Kelvin waves, and the co-rotating uniformm vortices. These are achieved by using relative variational methods and spectral analysis. Thus, we extend Arnol'd's idea for stability problems in [1965, 1969] to a non-smooth symmetric setting and also relate that to the usual linear stability analysis.Supported by National Science Foundation under grant DMS-8501746Dedicated to the memory of my grandmother, Lang-Chang Lee Wan