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Dynamic growth estimates of maximum vorticity for 3D incompressible Euler equations and the SQG model
1. | Caltech, Applied and Comput. Math, 9-94, Pasadena, CA 91125, United States, United States |
References:
[1] |
J. T. Beale, T. Kato and A. J. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys., 94 (1984), 61-66.
doi: 10.1007/BF01212349. |
[2] |
P. Constantin, C. Fefferman and A. Majda, Geometric constraints on potentially singular solutions for the 3-D Euler equation, Commun. PDE, 21 (1996), 559-571. |
[3] |
P. Constantin, A. J. Majda and E. G. Tabak, Singular front formation in a model for quasigeostrophic flow, Phys. Fluids, 6 (1994), 9-11.
doi: 10.1063/1.868050. |
[4] |
P. Constantin, Q. Nie and N. Schörghofer, Nonsingular surface quasi- geostrophic flow, Phys. Lett. A, 241 (1998), 168-172.
doi: 10.1016/S0375-9601(98)00108-X. |
[5] |
D. Cordoba, Nonexistence of simple hyperbolic bolw-up for the quasi-geostrophic equation, Ann. of Math. (2), 148 (1998), 1135-1152.
doi: 10.2307/121037. |
[6] |
D. Cordoba and C. Fefferman, On the collapse of tubes carried by 3D incompressible flows, Commun. Math. Phys., 222 (2001), 293-298.
doi: 10.1007/s002200100502. |
[7] |
D. Cordoba and C. Fefferman, Growth of solutions for QG and 2D Euler equations, J. Amer. Math. Soc., 15 (2002), 665-670.
doi: 10.1090/S0894-0347-02-00394-6. |
[8] |
J. Deng, T. Y. Hou and X. Yu, Geometric properties and nonblowup of 3D incompressible Euler flow, Comm. PDE, 30 (2005), 225-243.
doi: 10.1081/PDE-200044488. |
[9] |
J. Deng, T. Y. Hou and X. Yu, Improved geometric conditions for non-blowup of the 3D incompressible Euler equation, Comm. PDE, 31 (2006), 293-306.
doi: 10.1080/03605300500358152. |
[10] |
J. Deng, T. Y. Hou, R. Li and X. Yu, Level set dynamics and non-blowup of the 2D quasi-geostrophic equation, Methods and Applications of Analysis, 13 (2006), 157-180. |
[11] |
T. Y. Hou, Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations, Acta Numerica, 18 (2009), 277-346.
doi: 10.1017/S0962492906420018. |
[12] |
T. Y. Hou and R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations, J. Nonlinear Science, 16 (2006), 639-664.
doi: 10.1007/s00332-006-0800-3. |
[13] |
T. Y. Hou and R. Li, Blowup or no blowup? The interplay between theory and numerics, Phisica D, 237 (2008), 1937-1944.
doi: 10.1016/j.physd.2008.01.018. |
[14] |
R. M. Kerr, Evidence for a singularity of the three-dimensional, incompressible Euler equations, Phys. Fluids A, 5 (1993), 1725-1746.
doi: 10.1063/1.858849. |
[15] |
A. J. Majda and A. L. Bertozzi, "Vorticity and Incompressible Flow," Cambridge Texts in Applied Mathematics, 27, Cambridge University Press, Cambridge, 2002. |
[16] |
K. Ohkitani and M. Yamada, Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow, Phys. Fluids, 9 (1997), 876-882. |
show all references
References:
[1] |
J. T. Beale, T. Kato and A. J. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys., 94 (1984), 61-66.
doi: 10.1007/BF01212349. |
[2] |
P. Constantin, C. Fefferman and A. Majda, Geometric constraints on potentially singular solutions for the 3-D Euler equation, Commun. PDE, 21 (1996), 559-571. |
[3] |
P. Constantin, A. J. Majda and E. G. Tabak, Singular front formation in a model for quasigeostrophic flow, Phys. Fluids, 6 (1994), 9-11.
doi: 10.1063/1.868050. |
[4] |
P. Constantin, Q. Nie and N. Schörghofer, Nonsingular surface quasi- geostrophic flow, Phys. Lett. A, 241 (1998), 168-172.
doi: 10.1016/S0375-9601(98)00108-X. |
[5] |
D. Cordoba, Nonexistence of simple hyperbolic bolw-up for the quasi-geostrophic equation, Ann. of Math. (2), 148 (1998), 1135-1152.
doi: 10.2307/121037. |
[6] |
D. Cordoba and C. Fefferman, On the collapse of tubes carried by 3D incompressible flows, Commun. Math. Phys., 222 (2001), 293-298.
doi: 10.1007/s002200100502. |
[7] |
D. Cordoba and C. Fefferman, Growth of solutions for QG and 2D Euler equations, J. Amer. Math. Soc., 15 (2002), 665-670.
doi: 10.1090/S0894-0347-02-00394-6. |
[8] |
J. Deng, T. Y. Hou and X. Yu, Geometric properties and nonblowup of 3D incompressible Euler flow, Comm. PDE, 30 (2005), 225-243.
doi: 10.1081/PDE-200044488. |
[9] |
J. Deng, T. Y. Hou and X. Yu, Improved geometric conditions for non-blowup of the 3D incompressible Euler equation, Comm. PDE, 31 (2006), 293-306.
doi: 10.1080/03605300500358152. |
[10] |
J. Deng, T. Y. Hou, R. Li and X. Yu, Level set dynamics and non-blowup of the 2D quasi-geostrophic equation, Methods and Applications of Analysis, 13 (2006), 157-180. |
[11] |
T. Y. Hou, Blow-up or no blow-up? A unified computational and analytic approach to 3D incompressible Euler and Navier-Stokes equations, Acta Numerica, 18 (2009), 277-346.
doi: 10.1017/S0962492906420018. |
[12] |
T. Y. Hou and R. Li, Dynamic depletion of vortex stretching and non-blowup of the 3-D incompressible Euler equations, J. Nonlinear Science, 16 (2006), 639-664.
doi: 10.1007/s00332-006-0800-3. |
[13] |
T. Y. Hou and R. Li, Blowup or no blowup? The interplay between theory and numerics, Phisica D, 237 (2008), 1937-1944.
doi: 10.1016/j.physd.2008.01.018. |
[14] |
R. M. Kerr, Evidence for a singularity of the three-dimensional, incompressible Euler equations, Phys. Fluids A, 5 (1993), 1725-1746.
doi: 10.1063/1.858849. |
[15] |
A. J. Majda and A. L. Bertozzi, "Vorticity and Incompressible Flow," Cambridge Texts in Applied Mathematics, 27, Cambridge University Press, Cambridge, 2002. |
[16] |
K. Ohkitani and M. Yamada, Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow, Phys. Fluids, 9 (1997), 876-882. |
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