Hölder Continuity of Solutions of Supercritical Dissipative Hydrodynamic Transport Equations
Constantin, Peter ; Wu, Jiahong
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009), p. 159-180 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2009__26_1_159_0,
     author = {Constantin, Peter and Wu, Jiahong},
     title = {H\"older Continuity of Solutions of Supercritical Dissipative Hydrodynamic Transport Equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {26},
     year = {2009},
     pages = {159-180},
     doi = {10.1016/j.anihpc.2007.10.002},
     mrnumber = {2483817},
     zbl = {1163.76010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_1_159_0}
}

Constantin, Peter; Wu, Jiahong. Hölder Continuity of Solutions of Supercritical Dissipative Hydrodynamic Transport Equations. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 159-180. doi : 10.1016/j.anihpc.2007.10.002. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_1_159_0/

[1] Caffarelli L., Silvestre L., An Extension Problem Related to the Fractional Laplacian, arXiv: math.AP/0608640. | Zbl 1143.26002

[2] Caffarelli L., Vasseur A., Drift Diffusion Equations With Fractional Diffusion and the Quasi-Geostrophic Equation, arXiv: math.AP/0608447.

[3] Chae D., On the Regularity Conditions for the Dissipative Quasi-Geostrophic Equations, SIAM J. Math. Anal. 37 (2006) 1649-1656. | MR 2215601 | Zbl 1141.76010

[4] Chae D., Lee J., Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations, Commun. Math. Phys. 233 (2003) 297-311. | MR 1962043 | Zbl 1019.86002

[5] Chen Q., Miao C., Zhang Z., A New Bernstein Inequality and the 2D Dissipative Quasi-Geostrophic Equation, Commun. Math. Phys. 271 (2007) 821-838. | MR 2291797 | Zbl 1142.35069

[6] Constantin P., Euler Equations, Navier-Stokes Equations and Turbulence. Mathematical Foundation of Turbulent Viscous Flows, in: Lecture Notes in Math., vol. 1871, Springer, Berlin, 2006, pp. 1-43. | MR 2196360 | Zbl pre05551754

[7] Constantin P., Cordoba D., Wu J., On the Critical Dissipative Quasi-Geostrophic Equation, Indiana Univ. Math. J. 50 (2001) 97-107. | MR 1855665 | Zbl 0989.86004

[8] Constantin P., Majda A., Tabak E., Formation of Strong Fronts in the 2-D Quasi-Geostrophic Thermal Active Scalar, Nonlinearity 7 (1994) 1495-1533. | MR 1304437 | Zbl 0809.35057

[9] Constantin P., Wu J., Behavior of Solutions of 2D Quasi-Geostrophic Equations, SIAM J. Math. Anal. 30 (1999) 937-948. | MR 1709781 | Zbl 0957.76093

[10] Constantin P., Wu J., Regularity of Hölder Continuous Solutions of the Supercritical Quasi-Geostrophic Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (6) (2008) 1103-1110. | Numdam | MR 2466323 | Zbl 1149.76052

[11] Córdoba A., Córdoba D., A Maximum Principle Applied to Quasi-Geostrophic Equations, Commun. Math. Phys. 249 (2004) 511-528. | MR 2084005 | Zbl pre02158321

[12] Held I., Pierrehumbert R., Garner S., Swanson K., Surface Quasi-Geostrophic Dynamics, J. Fluid Mech. 282 (1995) 1-20. | MR 1312238 | Zbl 0832.76012

[13] T. Hmidi, S. Keraani, On the global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces, Adv. Math., in press. | MR 2349714 | Zbl 1119.76070

[14] Ju N., The Maximum Principle and the Global Attractor for the Dissipative 2D Quasi-Geostrophic Equations, Commun. Math. Phys. 255 (2005) 161-181. | MR 2123380 | Zbl 1088.37049

[15] Kiselev A., Nazarov F., Volberg A., Global Well-Posedness for the Critical 2D Dissipative Quasi-Geostrophic Equation, Invent. Math. 167 (2007) 445-453. | MR 2276260 | Zbl 1121.35115

[16] Marchand F., Lemarié-Rieusset P. G., Solutions Auto-Similaires Non Radiales Pour L'équation Quasi-Géostrophique Dissipative Critique, C. R. Math. Acad. Sci. Paris, Ser. I 341 (2005) 535-538. | MR 2181389 | Zbl 1155.76320

[17] Pedlosky J., Geophysical Fluid Dynamics, Springer, New York, 1987. | Zbl 0713.76005

[18] S. Resnick, Dynamical problems in nonlinear advective partial differential equations, Ph.D. thesis, University of Chicago, 1995.

[19] Schonbek M., Schonbek T., Asymptotic Behavior to Dissipative Quasi-Geostrophic Flows, SIAM J. Math. Anal. 35 (2003) 357-375. | MR 2001105 | Zbl 1126.76386

[20] Schonbek M., Schonbek T., Moments and Lower Bounds in the Far-Field of Solutions to Quasi-Geostrophic Flows, Discrete Contin. Dyn. Syst. 13 (2005) 1277-1304. | MR 2166670 | Zbl 1091.35070

[21] Wu J., The Quasi-Geostrophic Equation and Its Two Regularizations, Comm. Partial Differential Equations 27 (2002) 1161-1181. | MR 1916560 | Zbl 1012.35067

[22] Wu J., Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces, SIAM J. Math. Anal. 36 (2004/2005) 1014-1030. | MR 2111923 | Zbl 1083.76064

[23] Wu J., The Quasi-Geostrophic Equation With Critical Or Supercritical Dissipation, Nonlinearity 18 (2005) 139-154. | MR 2109471 | Zbl 1067.35002

[24] Wu J., Existence and Uniqueness Results for the 2-D Dissipative Quasi-Geostrophic Equation, Nonlinear Anal. 67 (2007) 3013-3036. | MR 2347594 | Zbl 1122.76014