The dissipative quasi-geostrophic equation in weak Morrey spaces

Acta Mathematica Sinica, English Series

Volumn 24, Issue 2, 2008, Pages 253-266

  Yuan, Bao Quan ^a  

^a HENAN POLYTECHNIC UNIVERSITY   (China)

Author keywords

Dissipative quasi geostrophic equation; Global well posedness; Weak Morrey spaces

Indexed keywords

EID: 40549112019     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-007-0973-1     Document Type: Article

References (22)

1. Constantin, P., Majda, A. J., Tabak, E.: Formation of strongfronts in the 2-D quasi-geostrophic thermal active scalar. Nonlinearity, 7, 1495-1533 (1994)
2. Pedlosky, J.: Geophysical fluid dynamics, Springer-Verlag, New York, 1987
3. Charney, J., Phillips, N.: Numerical integrations of the quasi-geostrophi equations for barotropic and baroclinic flows. J. Meteorol., 10, 71-99 (1953)
4. Held, I., Pierrehumbert, R., Garner, S., Swanson, K.: Surface quasi-geostrophic dynamics. J. Fluid Mech., 282, 1-20 (1995)
5. Fefferman, C. L.: Existence and smoothness of the Navier-Stokes equation, Millennium Problems, http://www.claymath.org/millennium/Navier-StokesEquations/ navierstokes.pdf, 2000
6. p data. Electron. J. Differential Equations, 2001, 1-13 (2001)
7. Wu, J. H.: Quasi-geostrophic-type equations with initial data in Morrey spaces. Nonlinearity, 10, 1409-1420 (1997)
8. Wu, J. H.: Quasi-geostrophic type equations with weak initial data, Electron. J. Differential Equations, 1998, 1-10 (1998)
9. Wu, J. H.: Solutions of the 2D quasi-geostrophic equation in Hölder spaces. Nonlinear Analysis, 62, 579-594 (2005)
10. Chae, D. H.: The quasi-geostrophic equations in the Triebel-Lizorkin spaces. Nonlinearity, 16, 479-495 (2003)
11. Constantin, P., Wu, J. H.: Behavior of solutions of 2D quasi-geostrophic equations. SIAM J. Math. Anal., 30, 737-948 (1999)
12. Zhang, Z. F.: Well-posedness for the 2D dissipative quasi-geostrophic equations in the Besov space. Science in China, Series A: Mathematics, 48(12), 1646-1655 (2005)
13. Constantin, P., Córdoba, D., Wu, J. H.: On the critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J., 50, 97-107 (2001)
14. Chae, D., Lee, J.: Global well-posedness in the super-critical dissipative quasi-geostrophic equations. Commun. Math. Phys., 233, 297-311 (2003)
15. Córdoba, A., Córdoba, D.: A mximum principle applied to quasi-geostrophic equations. Commun. Math. Phys., 249, 511-528 (2004)
16. Yuan, B. Q.: Mathematical methods for incompressible hydrodynamic and magneto-hydrodynamic equations, Ph.D thesis, China acadmy of engineering and physics, Beijing, 2005
17. Miao, C. X., Yuan, B. Q.: Weak Morrey Spaces and Strong Solutions to the Navier-Stokes Equations, Preprint
18. Miao, C. X., Yuan, B. Q., Zhang, B.: Well-posedness of the Cauchy problem for the fractional power dissipative equations, 1-30, Preprint
19. Lorentz, G. G.: Some new functional spaces. Ann. of Math., 1, 37-55 (1950)
20. Miao, C. X.: Harmonic analysis and application to partial differential equations, Science Press, Beijing, 2004, second edition
21. Stein, E., Weiss, G.: Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971
22. Giga, Y., Miyakawa, T., Osada, H.: Two-dimensional Navier-Stokes flow with measures as initial vorticity. Arch. Rat. Mech. Anal., 104, 223-250 (1988)