Eventual regularization for the slightly supercritical quasi-geostrophic equation
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, pp. 693-704.

We prove that weak solutions of the slightly supercritical quasi-geostrophic equation become smooth for large time. The proof uses ideas from a recent article of Caffarelli and Vasseur and is based on an argument in the style of De Giorgi.

Dans cet article, nous montrons que les solutions faibles de l'équation quasi-géostrophique légèrement sur-critique deviennent régulières en temps grand. La démonstration utilise des idées d'un article récent de Caffarelli et Vasseur et repose sur un argument de type de De Giorgi.

@article{AIHPC_2010__27_2_693_0,
     author = {Silvestre, Luis},
     title = {Eventual regularization for the slightly supercritical quasi-geostrophic equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {693--704},
     publisher = {Elsevier},
     volume = {27},
     number = {2},
     year = {2010},
     doi = {10.1016/j.anihpc.2009.11.006},
     mrnumber = {2595196},
     zbl = {1187.35186},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/}
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Silvestre, Luis. Eventual regularization for the slightly supercritical quasi-geostrophic equation. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 2, pp. 693-704. doi : 10.1016/j.anihpc.2009.11.006. http://www.numdam.org/articles/10.1016/j.anihpc.2009.11.006/

[1] Luis Caffarelli, Luis Silvestre, An extension problem related to the fractional laplacian, Comm. Partial Differential Equations 32 no. 7–9 (2007), 1245-1260 | MR | Zbl

[2] Luis Caffarelli, Alexis Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, Ann. of Math., in press | MR

[3] P. Constantin, J. Wu, Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Ann. Inst. H. Poincare Anal. Non Lineaire 25 no. 6 (2008), 1103-1110 | EuDML | Numdam | MR | Zbl

[4] P. Constantin, J. Wu, Hölder continuity of solutions of supercritical dissipative hydrodynamic transport equations, Ann. Inst. H. Poincare Anal. Non Lineaire 26 (2009), 159-180 | EuDML | Numdam | MR | Zbl

[5] Peter Constantin, Jiahong Wu, Behavior of solutions of 2D quasi-geostrophic equations, SIAM J. Math. Anal. 30 no. 5 (1999), 937-948 | MR | Zbl

[6] Antonio Córdoba, Diego Córdoba, A maximum principle applied to quasi-geostrophic equations, Comm. Math. Phys. 249 no. 3 (2004), 511-528 | MR | Zbl

[7] A. Kiselev, F. Nazarov, A. Volberg, Global well-posedness for the critical 2D dissipative quasi-geostrophic equation, Invent. Math. 167 no. 3 (2007), 445-453 | MR | Zbl

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