Geodesic
The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation
Castro, Ángel1 ; Córdoba, Diego1 ; Zheng, Fan1
1 Instituto de Ciencias Matemáticas ICMAT-CSIC-UAM-UCM-UC3M, 28049, Madrid, Spain
Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1583-1603

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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.

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DOI : 10.1016/j.anihpc.2020.12.005
Keywords: Surface Quasi-geostrophic, Normal forms, Rotating solutions

Castro, Ángel 1 ; Córdoba, Diego 1 ; Zheng, Fan 1

1 Instituto de Ciencias Matemáticas ICMAT-CSIC-UAM-UCM-UC3M, 28049, Madrid, Spain 
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     author = {Castro, \'Angel and C\'ordoba, Diego and Zheng, Fan},
     title = {The lifespan of classical solutions for the inviscid {Surface} {Quasi-geostrophic} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1583--1603},
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Castro, Ángel; Córdoba, Diego; Zheng, Fan. The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation. Annales de l'I.H.P. Analyse non linéaire, septembre – octobre 2021, Tome 38 (2021) no. 5, pp. 1583-1603. doi: 10.1016/j.anihpc.2020.12.005

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