On Existence and Space-Time Behavior of Dissipative 2D Quasi-Geostrophic Flows

Existence is proved for dissipative subcritical 2D quasi-geostrophic flows with a specific pointwise behavior in space-time. First we treat flows with small initial data, employing only elementary estimates or convolution integrals. Our results extend those proved in [7] and [12] for 2D Navier Stokes flows. We then prove the specific space-time behavior mentioned above is also interpreted in a framework of L(p)-like function spaces with 2/3 <= p <= x.