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Growth of solutions for QG and 2D Euler equations
Authors:
Diego Cordoba and Charles Fefferman
Journal:
J. Amer. Math. Soc. 15 (2002), 665-670
MSC (1991):
Primary 76B03, 35Q30; Secondary 35Q35, 76W05
Posted:
February 27, 2002
MathSciNet review:
1896236
Full-text PDF Free Access
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Abstract: We study the rate of growth of sharp fronts of the Quasi-geostrophic equation and 2D incompressible Euler equations. The development of sharp fronts are due to a mechanism that piles up level sets very fast. Under a semi-uniform collapse, we obtain a lower bound on the minimum distance between the level sets.
- 1.
Peter
Constantin, Andrew
J. Majda, and Esteban
Tabak, Formation of strong fronts in the 2-D quasigeostrophic
thermal active scalar, Nonlinearity 7 (1994),
no. 6, 1495–1533. MR 1304437
(95i:76107)
- 2.
Peter
Constantin, Qing
Nie, and Norbert
Schörghofer, Nonsingular surface quasi-geostrophic flow,
Phys. Lett. A 241 (1998), no. 3, 168–172. MR 1613907
(99a:76031), http://dx.doi.org/10.1016/S0375-9601(98)00108-X
- 3.
Diego
Cordoba, Nonexistence of simple hyperbolic blow-up for the
quasi-geostrophic equation, Ann. of Math. (2) 148
(1998), no. 3, 1135–1152. MR 1670077
(2000j:76020), http://dx.doi.org/10.2307/121037
- 4.
D. Cordoba and C. Fefferman.
Behavior of several 2D fluid equations in singular scenarios.
Proc. Nat. Acad. Sci. USA, 98:4311-4312, 2001. CMP 2001:10
- 5.
D. Cordoba and C. Fefferman.
Scalars convected by a 2D incompressible flow.
Comm. Pure Appl. Math., 55 (2):255-260, 2001. CMP 2002:04
- 6.
Diego
Cordoba and Christiane
Marliani, Evolution of current sheets and regularity of ideal
incompressible magnetic fluids in 2D, Comm. Pure Appl. Math.
53 (2000), no. 4, 512–524. MR 1733694
(2000i:76130), http://dx.doi.org/10.1002/(SICI)1097-0312(200004)53:4<512::AID-CPA4>3.3.CO;2-I
- 7.
Andrew
J. Majda and Esteban
G. Tabak, A two-dimensional model for quasigeostrophic flow:
comparison with the two-dimensional Euler flow, Phys. D
98 (1996), no. 2-4, 515–522. Nonlinear
phenomena in ocean dynamics (Los Alamos, NM, 1995). MR 1422288
(97g:86005), http://dx.doi.org/10.1016/0167-2789(96)00114-5
- 8.
Koji
Ohkitani and Michio
Yamada, Inviscid and inviscid-limit behavior of a surface
quasigeostrophic flow, Phys. Fluids 9 (1997),
no. 4, 876–882. MR 1437554
(97m:76032), http://dx.doi.org/10.1063/1.869184
- 1.
- P. Constantin, A. J. Majda, and E. Tabak.
Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar.
Nonlinearity, 7:1495-1533, 1994. MR 95i:76107
- 2.
- P. Constantin, Q. Nie, and N. Schorghofer.
Nonsingular surface-quasi-geostrophic flow.
Phys. Lett. A, 24:168-172, 1998. MR 99a:76031
- 3.
- D. Cordoba.
Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation.
Ann. of Math., 148 (3):1135-1152, 1998. MR 2000j:76020
- 4.
- D. Cordoba and C. Fefferman.
Behavior of several 2D fluid equations in singular scenarios.
Proc. Nat. Acad. Sci. USA, 98:4311-4312, 2001. CMP 2001:10
- 5.
- D. Cordoba and C. Fefferman.
Scalars convected by a 2D incompressible flow.
Comm. Pure Appl. Math., 55 (2):255-260, 2001. CMP 2002:04
- 6.
- D. Cordoba and C. Marliani.
Evolution of current sheets and regularity of ideal incompressible magnetic fluids in 2D.
Comm. Pure Appl. Math., 53 (4):512-524, 2000. MR 2000i:76130
- 7.
- A. Majda and E. Tabak.
A two-dimensional model for quasi-geostrophic flow: comparison with the two-dimensional Euler flow.
Physica D, 98:515-522, 1996. MR 97g:86005
- 8.
- K. Ohkitani and M. Yamada.
Inviscid and inviscid-limit behavior of a surface quasi-geostrophic flow.
Phys. Fluids, 9:876-882, 1997. MR 97m:76032
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Additional Information
Diego Cordoba
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Address at time of publication:
Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Email:
dcg@math.princeton.edu
Charles Fefferman
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08540
Email:
cf@math.princeton.edu
DOI:
http://dx.doi.org/10.1090/S0894-0347-02-00394-6
PII:
S 0894-0347(02)00394-6
Keywords:
Quasi-geostrophic,
Euler and MHD equations,
front formation,
singularities
Received by editor(s):
March 25, 2001
Posted:
February 27, 2002
Additional Notes:
This work was initially supported by the American Institute of Mathematics.
The second author was supported in part by NSF Grant DMS 0070692.
Article copyright:
© Copyright 2002 American Mathematical Society
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