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In this paper, we construct smooth traveling counter-rotating vortex pairs with circular supports for the generalized surface quasi-geostrophic equation. These vortex pairs are analogues of the Lamb dipoles for the 2D incompressible Euler equation. The solutions are obtained by maximization of the energy over some appropriate classes of admissible functions. We establish the uniqueness of maximizers and compactness of maximizing sequences in our variational setting. Using these facts, we further prove the orbital stability of the circular vortex pairs for the generalized surface quasi-geostrophic equation.

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