We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation ϵ from a radial stationary solution . We use a modified energy method to prove the existence time of classical solutions from to a time scale of . Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time and space.
Cite this article
Ángel Castro, Diego Córdoba, Fan Zheng, The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, pp. 1583–1603DOI 10.1016/J.ANIHPC.2020.12.005