Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Nonlinearity

Volumn 25, Issue 5, 2012, Pages 1525-1535

  Dabkowski, Michael ^a   Kiselev, Alexander ^a   Vicol, Vlad ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84862095067     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/25/5/1525     Document Type: Article

References (17)

1. Caffarelli L and Vasseur A 2010 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation Ann. Math. 171 1903-30
2. Chae D, Constantin P and Wu J 2011 Inviscid models generalizing the 2D Euler and the surface quasi-geostrophic equations Arch. Ration. Mech. Anal. 202 35-62
3. Chae D, Constantin P and Wu J 2010 Dissipative models generalizing the 2D Navier-Stokes and the SQG equations Indiana Univ. Math. J. submitted (arXiv:1011.0171v1) [math.AP])
4. Córdoba A and Córdoba D 2004 A maximum principle applied to quasi-geostrophic equations Commun. Math. Phys. 249 511-28 (Pubitemid 39216537)
5. Constantin P, Majda A J and Tabak E 1994 Formation of strong fronts in the 2-D quasi-geostrophic thermal active scalar Nonlinearity 7 1495-533
6. Constantin P and Wu J 2008 Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation Ann. Inst. Henri Poincaré Anal. Non Linéaire 25 1103-10
7. Dabkowski 2011 Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation Geom. Funct. Anal. 21 1-13
8. Dabkowski M, Kiselev A, Silvestre L and Vicol V 2012 Global well-posedness of slightly supercritical active scalar equations arXiv:1203.6302v1
9. Dong H 2010 Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness Discrete Contin. Dyn. Syst. 26 1197-211
10. Dong H and Pavlovic N 2009 Regularity criteria for the dissipative quasi-geostrophic equations in Holder spaces Commun. Math. Phys. 290 801-12
11. Kiselev A 2011 Nonlocal maximum principles for active scalars Adv. Math. 227 1806-26
12. Kiselev A and Nazarov F 2010 A variation on a theme of Caffarelli and Vasseur Zap. Nauchn. Sem. POMI 370 58-72
13. Kiselev A, Nazarov F and Volberg A 2007 Global well-posedness for the critical 2D dissipative quasi-geostrophic equation Invent. Math. 167 445-53
14. Resnick S 1995 Dynamical problems in nonlinear advective partial differential equations PhD Thesis University of Chicago
15. Silvestre L 2010 Eventual regularization for the slightly supercritical quasi-geostrophic equation Ann. Inst. Henri Poincaré Anal. Non Linéaire 27 693-704
16. Stein E M 1993 Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals (Princeton Mathematical Series vol 43) (Princeton, NJ: Princeton University Press)
17. Tao T 2009 Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation Anal. Partial Diff. Eqns 2 361-6