Blow up for the generalized surface quasi-geostrophic equation with supercritical dissipation

Communications in Mathematical Physics

Volumn 286, Issue 1, 2009, Pages 111-124

  Li, Dong ^a   Rodrigo, Jose ^b  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58149492604     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0585-3     Document Type: Article

References (20)

1. P. Balodis A. Córdoba 2007 Inequality for Riesz transforms implying blow-up for some nonlinear and nonlocal transport equations Adv. Math. 214 1 1 39
2. Bertozzi A.L., Majda A.J.: Vorticity and the Mathematical Theory of Incompressible Fluid Flow. Cambridge Univ. Press, Cambridge (2002)
3. Caffarelli, L., Vasseur, A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, http://arxiv.org/abs/math/0608447, 2006
4. P. Constantin Q. Nie N. Schörghofer 1998 Nonsingular surface quasi-geostrophic flow Phys. Lett. A 241 168 172
5. P. Constantin D. Córdoba J. Wu 2001 On the critical dissipative quasi-geostrophic equation Indiana Univ. Math. J. 50 97 107
6. P. Constantin P. Lax A. Majda 1985 A simple one-dimensional model for the three-dimensional vorticity Comm. Pure Appl. Math. 38 715 724
7. D. Córdoba 1998 Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation Ann. of Math. 148 1135 1152
8. A. Córdoba D. Córdoba M.A. Fontelos 2005 Formation of singularities for a transport equation with nonlocal velocity Ann. of Math. 162 3 1375 1387
9. A. Córdoba D. Córdoba M.A. Fontelos 2006 Integral inequalities for the Hilbert transform applied to a nonlocal transport equation J. Math. Pures Appl. 86 6 529 540
10. P. Constantin A.J. Majda E. Tabak 1994 Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar Nonlinearity 7 6 1495 1533
11. H. Dong D. Li 2008 Finite time singularities for a class of generalized surface quasi-geostrophic equations Proc. Amer. Math. Soc. 136 2555 2563
12. S. De Gregorio 1996 A partial differential equation arising in a 1D model for the 3D vorticity equation Math. Methods Appl. Sci. 19 1233 1255
13. N. Ju 2007 Dissipative quasi-geostrophic equation: local well-posedness, global regularity and similarity solutions Indiana Univ. Math. J. 56 1 187 206
14. A. Kiselev F. Nazarov A. Volberg 2007 Global well-posedness for the critical 2D dissipative quasi- geostrophic equation Invent. Math. 167 3 445 453
15. D. Li J. Rodrigo 2008 Blow up of solutions for a 1D transport equation with nonlocal velocity and supercritical dissipation Adv. Math. 217 6 2563 2568
16. A.J. Majda E.G. Tabak 1996 A two-dimensional model for quasi-geostrophic flow: comparison with the two-dimensional Euler flow Physica D. 98 515 522
17. K. Ohkitani M. Yamada 1997 Inviscid and inviscid-limit behavior of a surface quasi-geostrophic flow Phys. Fluids 9 876 882
18. Pedlosky J.: Geophysical Fluid Dynamics. Springer-Verlag, New York (1987)
19. G. Pólya 1918 Uber die Nullstellen gewisser ganzer Funktionen Math Z. 2 3-4 352 383
20. Pólya, G.: Collected papers. Vol. II: Location of zeros, R. P. Boas, ed., Mathematicians of Our Time, Vol. 8, Cambridge, MA-London: MIT Press, 1974