Eventual regularization for the slightly supercritical quasi-geostrophic equation
Silvestre, Luis
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 693-704 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

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.

@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},
     volume = {27},
     year = {2010},
     pages = {693-704},
     doi = {10.1016/j.anihpc.2009.11.006},
     mrnumber = {2595196},
     zbl = {1187.35186},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2010__27_2_693_0}
}

Silvestre, Luis. Eventual regularization for the slightly supercritical quasi-geostrophic equation. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) pp. 693-704. doi : 10.1016/j.anihpc.2009.11.006. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_2_693_0/

[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 2354493 | Zbl 1143.26002

[2] Luis Caffarelli, Alexis Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, Ann. of Math., in press | MR 2680400

[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 | Numdam | MR 2466323 | Zbl 1149.76052

[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 | Numdam | MR 2483817 | Zbl 1163.76010

[5] Peter Constantin, Jiahong Wu, Behavior of solutions of 2D quasi-geostrophic equations, SIAM J. Math. Anal. 30 no. 5 (1999), 937-948 | MR 1709781 | Zbl 0957.76093

[6] Antonio Córdoba, Diego Córdoba, A maximum principle applied to quasi-geostrophic equations, Comm. Math. Phys. 249 no. 3 (2004), 511-528 | MR 2084005 | Zbl 1309.76026

[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 2276260 | Zbl 1121.35115