Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalized viscosity: A numerical study

Nonlinearity

Volumn 23, Issue 12, 2010, Pages 3029-3051

  Ohkitani, Koji ^a   Sakajo, Takashi ^b,c  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b HOKKAIDO UNIVERSITY   (Japan)

^c JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650136818     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/23/12/003     Document Type: Article

References (27)

1. Alibaud N, Imbert C and Karch G 2010 Asymptotic properties of entropy solutions to fractal burgers equation SIAM J. Math. Anal. 42 354-76
2. Bardos C, Penel P, FrischUand Sulem PL 1979 Modified dissipativity for a non-linear evolution equation arising in turbulence Arch. Ration. Mech. Anal. 71 237-56
3. Constantin P, NieQand Schörghofer 1998 Nonsingular surface quasi-geostrophic flowPhys. Lett.A241 168-72
4. Caffarelli L and Vasseur A 2010 Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation Acta Math. to appear (arXiv:math/0608447)
5. Chae D 2006 On the Regularity Conditions for the Dissipative Quasi-geostrophic Equations SIAM J. Math. Anal. 37 1649-56
6. Chan CH, CzubakMand Silvestre L 2010 Eventual regularization of the slightly supercritical fractional Burgers equation Discrete Contin. Dyn. Syst. 27 847-861
7. Constantin P 2008 Singular, weak and absent: solutions of the Euler equations Physica. D 237 1926-31
8. 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
9. Constantin P, Majda A J and Tabak E 1994 Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar Nonlinearity 7 1495-533
10. Constantin P, Majda A J and Tabak E 1994 Singular front formation in a model for quasigeostrophic flow Phys. Fluids 6 9-11
11. Cordoba A and Cordoba D 2004 A maximum principle applied to quasi-geostrophic equations Commun. Math. Phys. 249 511-28
12. Deng J, Hou TY, Li R and Yu X 2006 Level Set Dynamics and the Non-blowup of the 2D quasi-geostrophic equation Methods Appl. Anal. 13 157-80
13. Foias C, Hoang L, Olson E and Ziane M 2006 On the solutions to the normal form of the Navier-Stokes equations Indiana Univ. Math. J. 55 631-86
14. Foias C, Hoang L, Olson E and Ziane M 2009 The normal form of the Navier-Stokes equations in suitable normed spaces Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 1635-73
15. Foias C and Saut JC 1987 Linearization and normal form of the Navier-Stokes equations with potential forces Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4 1-47
16. Foias C and Saut JC 1982 Transformation fonctionnelle linéarisant les equation de Navier-Stokes C.R. Acad. Sci. Paris, Série I, Math. 23 325-7
17. Friedlander S, Pavlovic N and Vicol V 2009 Nonlinear instability for the critically dissipative quasi-geostrophic equation Commun. Math. Phys. 292 797-810
18. Fujiwara H, Extend precision floating-point arithmetic library(Exflib) is available at http://www-an.acs.i.kyoto-u.ac.jp/~fujiwara/exflib/index.html
19. Kiselev A, Nazarov F and Volberg A2006 Global well-posedness for the critical 2D dissipative quasi-geostrophic equation Invent. Math. 167 445-53
20. Kiselev A, Nazarov F and Shterenberg R 2008 Blow Up and Regularity for Fractal Burgers Equation Dyn. Partial Diff. Eqns 5 211-40
21. Majda A J and Tabak E G 1996 A two-dimensional model for quasigeostrophic flow: comparison with the two-dimensional Euler flow Physica D 98 515-522
22. Niche CJ and Schonbek ME 2007 Decay of Weak Solutions to the 2D Dissipative Quasi-Geostrophic Equation Commun. Math. Phys. 276 93-115
23. Ohkitani K and Yamada M 1997 Inviscid and inviscid-limit behavior of a surface quasi-geostrophic flow Phys. Fluids 9 876-882
24. Silvestre L 2010 Eventual regularization for the slightly supercritical quasi-geostrophic equation Ann. Inst. Henri Poincaré, Anal. Non Linéaire 27 693-704
25. ShelleyMJ 1992 A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method J. Fluid Mech. 244 493-526
26. Sulem C, Sulem PL and Frisch H 1983 Tracing complex singularities with spectral methods J. Comput. Phys. 50 138-61
27. Wu J 2005 Global Solutions of the 2D Dissipative Quasi-Geostrophic Equation in Besov Spaces SIAM J. Math. Anal. 36 1014-30 (Pubitemid 40672799)