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arXiv · 2007.04692

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

Ángel Castro·Diego Córdoba·Fan Zheng
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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.

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Ángel Castro, Diego Córdoba, Fan Zheng. 2020-07-09. The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation. https://arxiv.org/abs/2007.04692

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