Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness
By Hongjie Dong. 2007
78 citations recorded by the source corpus.
We study the critical and super-critical dissipative quasi-geostrophic equations in $\bR^2$ or $\bT^2$. Higher regularity of mild solutions with arbitrary initial data in $H^{2-\gamma}$ is proved. As a corollary, we obtain a global existence result for the critical 2D quasi-geostrophic equations with periodic $\dot H^1$ data. Some decay in time estimates are also provided.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/82a7386133aeb377df8ca136c6f95882e10554e1
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In Applied Mathematics
- Michele Coti Zelati
- Vlad Vicol
- Hongjie Dong
- Doyoon Kim
- Nader Masmoudi
- T. Buckmaster
- Maria Colombo
- Martina Hofmanov'a
In Mathematical Physics
- Michele Coti Zelati
- Vlad Vicol
- Hongjie Dong
- Nader Masmoudi
- Doyoon Kim
- Maria Colombo
- Luis Silvestre
- T. Buckmaster
Citations in the corpus
- Well-posedness for a transport equation with nonlocal velocity (2008, background): “The author would like to thank Nicolai V. Krylov, Dong Li and the anonymous referee for many helpful comments on an earlier version the article.”
- On the global regularity for the supercritical SQG equation (2014, background): “Moreover, on [0, T1) the solution becomes smooth [12, 13].”