The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation

Abstract

We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation ϵ from a radial stationary solution θ=|x|. We use a modified energy method to prove the existence time of classical solutions from 1ϵ to a time scale of 1ϵ4. Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time and space.