Existence and Stability of Smooth Traveling Circular Pairs for the Generalized Surface Quasi-Geostrophic Equation

In this paper, we construct smooth travelling counter-rotating vortex pairs with circular supports for the generalized surface quasi-geostrophic equation. These are analogues of Lamb dipoles two-dimensional incompressible Euler The solutions obtained by maximization energy over some appropriate classes admissible functions. We establish uniqueness maximizers and compactness maximizing sequences in our variational setting. Using these facts, further prove orbital stability gSQG