Growth of solutions for QG and 2D Euler equations
HTML articles powered by AMS MathViewer
- by Diego Cordoba and Charles Fefferman
- J. Amer. Math. Soc. 15 (2002), 665-670
- DOI: https://doi.org/10.1090/S0894-0347-02-00394-6
- Published electronically: February 27, 2002
- PDF | Request permission
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.References
- 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, DOI 10.1088/0951-7715/7/6/001
- Peter Constantin, Qing Nie, and Norbert Schörghofer, Nonsingular surface quasi-geostrophic flow, Phys. Lett. A 241 (1998), no. 3, 168–172. MR 1613907, DOI 10.1016/S0375-9601(98)00108-X
- 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, DOI 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. 5 D. Cordoba and C. Fefferman. Scalars convected by a 2D incompressible flow. Comm. Pure Appl. Math., 55 (2):255-260, 2001.
- 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, DOI 10.1002/(SICI)1097-0312(200004)53:4<512::AID-CPA4>3.3.CO;2-I
- 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, DOI 10.1016/0167-2789(96)00114-5
- 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, DOI 10.1063/1.869184
Bibliographic 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
- MR Author ID: 627661
- Email: dcg@math.princeton.edu
- Charles Fefferman
- Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08540
- MR Author ID: 65640
- Email: cf@math.princeton.edu
- Received by editor(s): March 25, 2001
- Published electronically: 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. - © Copyright 2002 American Mathematical Society
- Journal: J. Amer. Math. Soc. 15 (2002), 665-670
- MSC (1991): Primary 76B03, 35Q30; Secondary 35Q35, 76W05
- DOI: https://doi.org/10.1090/S0894-0347-02-00394-6
- MathSciNet review: 1896236