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Navier--Stokes equations on a rapidly rotating sphere
1. | Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom |
References:
[1] |
M. A. H. Al-Jaboori and D. Wirosoetisno, Navier-Stokes equations on the $\beta$-plane, Discr. Contin. Dyn. Sys. B, 16 (2011), 687-701, arXiv:1009.4538.
doi: 10.3934/dcdsb.2011.16.687. |
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C. Cao, M. A. Rammaha and E. S. Titi, The Navier-Stokes equations on the rotating 2-$d$ sphere: Gevrey regularity and asymptotic degrees of freedom, ZAMP, 50 (1999), 341-360.
doi: 10.1007/PL00001493. |
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B. Cheng and A. Mahalov, Euler equations on a fast rotating sphere - time-averages and zonal flows, Eur. J. Mech. B/Fluids, 37 (2013), 48-58, arXiv:1108.2536v1.
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P. Constantin, C. Foias and R. Temam, On the dimension of the attractors in two-dimensional turbulence, Physica, 30 (1988), 284-296.
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C. Foias and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 87 (1989), 359-369.
doi: 10.1016/0022-1236(89)90015-3. |
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A. A. Il'in and A. N. Filatov, On unique solvability of the Navier-Stokes equations on the two-dimensional sphere, Soviet Math. Dokl., 38 (1989), 9-13. |
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A. A. Ilyin, Navier-Stokes equations on the rotating sphere. A simple proof of the attractor dimension estimate, Nonlinearity, 7 (1994), 31-39.
doi: 10.1088/0951-7715/7/1/002. |
[8] |
A. A. Il'yin, Partly dissipative semigroups generated by the Navier-Stokes system on two-dimensional manifolds, and their attractors, Russian Acad. Sci. Sb. Math., 78 (1994), 47-76; Orig: Ross. Akad. Nauk Matem. Sbornik, 184 (1993), 55-88.
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M. N. Jones, Spherical Harmonics and Tensors for Classical Field Theory, Research Studies Press, 1985. |
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National Institute for Standards and Technology, Digital library of mathematical functions, 2010,, URL , ().
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show all references
References:
[1] |
M. A. H. Al-Jaboori and D. Wirosoetisno, Navier-Stokes equations on the $\beta$-plane, Discr. Contin. Dyn. Sys. B, 16 (2011), 687-701, arXiv:1009.4538.
doi: 10.3934/dcdsb.2011.16.687. |
[2] |
C. Cao, M. A. Rammaha and E. S. Titi, The Navier-Stokes equations on the rotating 2-$d$ sphere: Gevrey regularity and asymptotic degrees of freedom, ZAMP, 50 (1999), 341-360.
doi: 10.1007/PL00001493. |
[3] |
B. Cheng and A. Mahalov, Euler equations on a fast rotating sphere - time-averages and zonal flows, Eur. J. Mech. B/Fluids, 37 (2013), 48-58, arXiv:1108.2536v1.
doi: 10.1016/j.euromechflu.2012.06.001. |
[4] |
P. Constantin, C. Foias and R. Temam, On the dimension of the attractors in two-dimensional turbulence, Physica, 30 (1988), 284-296.
doi: 10.1016/0167-2789(88)90022-X. |
[5] |
C. Foias and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal., 87 (1989), 359-369.
doi: 10.1016/0022-1236(89)90015-3. |
[6] |
A. A. Il'in and A. N. Filatov, On unique solvability of the Navier-Stokes equations on the two-dimensional sphere, Soviet Math. Dokl., 38 (1989), 9-13. |
[7] |
A. A. Ilyin, Navier-Stokes equations on the rotating sphere. A simple proof of the attractor dimension estimate, Nonlinearity, 7 (1994), 31-39.
doi: 10.1088/0951-7715/7/1/002. |
[8] |
A. A. Il'yin, Partly dissipative semigroups generated by the Navier-Stokes system on two-dimensional manifolds, and their attractors, Russian Acad. Sci. Sb. Math., 78 (1994), 47-76; Orig: Ross. Akad. Nauk Matem. Sbornik, 184 (1993), 55-88.
doi: 10.1070/SM1994v078n01ABEH003458. |
[9] |
M. N. Jones, Spherical Harmonics and Tensors for Classical Field Theory, Research Studies Press, 1985. |
[10] |
National Institute for Standards and Technology, Digital library of mathematical functions, 2010,, URL , ().
|
[11] |
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