The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation |
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| Institution: | 1. Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada;2. School of mathematical sciences, University of Chinese academy of sciences, Beijing, China;1. EPFL SB, Station 8, CH-1015 Lausanne, Switzerland;2. Departement Mathematik und Informatik, Universität Basel, Spiegelgasse 1, CH-4051 Basel, Switzerland;3. IMATI-CNR, via Ferrata 5, I-27100 Pavia, Italy;1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Brazil;2. Dipartimento di Matematica, Politecnico di Milano, Italy;1. Department of Mathematics, Texas A & M University, College Station, TX 77843-3368, USA;2. Department of Mathematics, University of North Carolina - Chapel Hill, Chapel Hill, NC 27599, USA;3. Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada;1. Politecnico di Torino, Dipartimento di Scienze Matematiche “G.L. Lagrange”, Corso Duca degli Abruzzi, 24, 10129, Torino, Italy;2. CNRS, Sorbonne Université, Inria, Université de Paris, Laboratoire Jacques-Louis Lions, Paris, France;3. Dipartimento di Matematica Tullio Levi-Civita, Università degli Studi di Padova, via Trieste 63, 35131 Padova, Italy;4. Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, 91190, Gif-sur-Yvette, France |
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| Abstract: | 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. |
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| Keywords: | Surface Quasi-geostrophic Normal forms Rotating solutions |
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