@article{AIHPC_2009__26_5_1607_0,
author = {Dong, Hongjie and Pavlovi\'c, Nata\v{s}A},
title = {A {Regularity} {Criterion} for the {Dissipative} {Quasi-Geostrophic} {Equations}},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {1607--1619},
year = {2009},
publisher = {Elsevier},
volume = {26},
number = {5},
doi = {10.1016/j.anihpc.2008.08.001},
mrnumber = {2566702},
zbl = {1176.35133},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2008.08.001/}
}
TY - JOUR AU - Dong, Hongjie AU - Pavlović, NatašA TI - A Regularity Criterion for the Dissipative Quasi-Geostrophic Equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 1607 EP - 1619 VL - 26 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2008.08.001/ DO - 10.1016/j.anihpc.2008.08.001 LA - en ID - AIHPC_2009__26_5_1607_0 ER -
%0 Journal Article %A Dong, Hongjie %A Pavlović, NatašA %T A Regularity Criterion for the Dissipative Quasi-Geostrophic Equations %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 1607-1619 %V 26 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2008.08.001/ %R 10.1016/j.anihpc.2008.08.001 %G en %F AIHPC_2009__26_5_1607_0
Dong, Hongjie; Pavlović, NatašA. A Regularity Criterion for the Dissipative Quasi-Geostrophic Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 5, pp. 1607-1619. doi: 10.1016/j.anihpc.2008.08.001
[1] L. Caffarelli, A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, preprint.
[2] , The Quasi-Geostrophic Equation in the Triebel-Lizorkin Spaces, Nonlinearity 16 (2) (2003) 479-495. | Zbl | MR
[3] , On the Regularity Conditions for the Dissipative Quasi-Geostrophic Equations, SIAM J. Math. Anal. 37 (5) (2006) 1649-1656. | Zbl | MR
[4] , , Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations, Commun. Math. Phys. 233 (2003) 297-311. | Zbl | MR
[5] , Théorèmes D'unicité Pour Le Système De Navier-Stokes Tridimensionnel, J. Anal. Math. 77 (1999) 27-50, (in French). | Zbl | MR
[6] , , , A New Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation, Commun. Math. Phys. 271 (3) (2007) 821-838. | Zbl | MR
[7] , , On the Regularity of Weak Solutions of the 3D Navier-Stokes Equations in , preprint, arXiv:math.AP/0708.3067. | MR
[8] , , , On the Critical Dissipative Quasi-Geostrophic Equation, Indiana Univ. Math. J. 50 (2001) 97-107. | Zbl | MR
[9] , , , Formation of Strong Fronts in the 2-D Quasigeostrophic Thermal Active Scalar, Nonlinearity 7 (6) (1994) 1495-1533. | Zbl | MR
[10] , , Behavior of Solutions of 2D Quasi-Geostrophic Equations, SIAM J. Math. Anal. 30 (1999) 937-948. | Zbl | MR
[11] P. Constantin, J. Wu, Hölder continuity of solutions of super-critical dissipative hydrodynamic transport equations, Ann. I. H. Poincaré - AN (2007), doi:10.1016/j.anihpc.2007.10.002. | Zbl | Numdam
[12] P. Constantin, J. Wu, Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Ann. I. H. Poincaré - AN (2007), doi:10.1016/j.anihpc.2007.10.001. | Zbl | Numdam
[13] , Density-Dependent Incompressible Viscous Fluids in Critical Spaces, Proc. Roy. Soc. Edinburgh Sect. A 133 (6) (2003) 1311-1334. | Zbl | MR
[14] , , A Remark on Regularity Criterion for the Dissipative Quasi-Geostrophic Equations, J. Math. Anal. Appl. (2007) 1212-1217. | Zbl | MR
[15] H. Dong, Dissipative quasi-geostrophic equations in critical Sobolev spaces: smoothing effect and global well-posedness, 2007, submitted for publication.
[16] , , Global Well-Posedness and a Decay Estimate for the Critical Dissipative Quasi-Geostrophic Equation in the Whole Space, Discrete Contin. Dyn. Syst. 21 (4) (2008) 1095-1101. | Zbl | MR
[17] H. Dong, D. Li, On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces, 2007, submitted for publication.
[18] , , , -Solutions of the Navier-Stokes Equations and Backward Uniqueness, Russian Math. Surveys 58 (2003). | Zbl | MR
[19] , Solutions for Semilinear Parabolic Equations in and Regularity of Weak Solutions of the Navier-Stokes System, J. Differential Equations 61 (1986) 186-212. | Zbl | MR
[20] , , Global Solutions of the Super-Critical 2D Quasi-Geostrophic Equation in Besov Spaces, Adv. Math. 214 (2) (2007) 618-638. | Zbl | MR
[21] , The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations, Commun. Math. Phys. 255 (1) (2005) 161-181. | Zbl | MR
[22] , , , Global Well-Posedness for the Critical 2D Dissipative Quasi-Geostrophic Equation, Invent. Math. 167 (3) (2007) 445-453. | Zbl | MR
[23] , On Uniqueness and Smoothness of Generalized Solutions to the Navier-Stokes Equations, Zapiski Nauchn. Seminar. POMI 5 (1967) 169-185. | Zbl | MR
[24] , Dissipative Quasi-Geostrophic Equation for Large Initial Data in the Critical Sobolev Space, Commun. Math. Phys. 267 (1) (2006) 141-157. | Zbl | MR
[25] , Geophysical Fluid Dynamics, Springer, New York, 1987. | Zbl
[26] , Un Teorema Di Unicità Per El Equazioni Di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959) 173-182. | Zbl | MR
[27] S. Resnick, Dynamical problems in nonlinear advective partial differential equations, Ph.D. thesis, University of Chicago, 1995.
[28] , On the Interior Regularity of Weak Solutions of the Navier-Stokes Equations, Arch. Ration. Mech. Anal. 9 (1962) 187-195. | Zbl | MR
[29] , Global Solutions of the 2D Dissipative Quasi-Geostrophic Equations in Besov Spaces, SIAM J. Math. Anal. 36 (3) (2004/2005) 1014-1030, (electronic). | Zbl | MR
[30] , Lower Bounds for an Integral Involving Fractional Laplacians and the Generalized Navier-Stokes Equations in Besov Spaces, Commun. Math. Phys. 263 (3) (2006) 803-831. | Zbl | MR
[31] , Existence and Uniqueness Results for the 2-D Dissipative Quasi-Geostrophic Equation, Nonlinear Anal. 67 (2007) 3013-3036. | Zbl | MR
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