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 $\epsilon$ from a radial stationary solution $\theta =|x|$. We use a modified energy method to prove the existence time of classical solutions from $\frac{1}{\epsilon }$ to a time scale of $\frac{1}{{\epsilon }^4}$. Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time and space.

25 pages

References in corpus (1)

• Global solutions for a family of GSQG front equations