Asymptotic Study of the 2D-DQGE Solutions

Abstract EN

We study the regularity of the solutions of the surface quasi-geostrophic equation with subcritical exponent 1 / 2 < α ≤ 1 .

We prove that if the initial data is small enough in the critical space H ˙ 2 - 2 α ( R 2 ) , then the regularity of the solution is of exponential growth type with respect to time and its H ˙ 2 - 2 α ( R 2 ) norm decays exponentially fast.

It becomes then infinitely differentiable with respect to time and has value in all homogeneous Sobolev spaces H ˙ s ( R 2 ) for s ≥ 2 - 2 α .

Moreover, we give some general properties of the global solutions.