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Divergence
Timeaverages of fast oscillatory systems
1.  School of Mathematical and Statistical Sciences, Arizona State University, Wexler Hall (PSA), Tempe, Arizona, 852871804, United States, United States 
References:
[1] 
W. Arendt, C. Batty, M. Hieber and F. Neubrander, "VectorValued Laplace Transforms and Cauchy Problems,", Monographs in Mathematics, 96 (2001). 
[2] 
A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3D Euler and NavierStokes equations for uniformly rotating fluids,, European J. Mechanics B Fluids, 15 (1996), 291. 
[3] 
A. Babin, A. Mahalov and B. Nicolaenko, Global splitting and regularity of rotating shallowwater equations,, European J. Mech. B Fluids, 16 (1997), 725. 
[4] 
H. Beirão da Veiga, On the barotropic motion of compressible perfect fluids,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 8 (1981), 317. 
[5] 
Bin Cheng, Singular limits and convergence rates of compressible Euler and rotating shallow water equations,, SIAM J. on Mathematical Analysis, 44 (2012), 1050. doi: 10.1137/11085147X. 
[6] 
Bin Cheng and Alex Mahalov, Euler equations on a fast rotating spheretimeaverages and zonal flows,, European J. Mech.  B/Fluids, 37 (2013), 48. doi: 10.1016/j.euromechflu.2012.06.001. 
[7] 
D. G. Ebin, The motion of slightly compressible fluids viewed as a motion with strong constraining force,, Ann. of Math. (2), 105 (1977), 141. 
[8] 
David G. Ebin, Motion of slightly compressible fluids in a bounded domain. I., Comm. Pure Appl. Math., 35 (1982), 451. doi: 10.1002/cpa.3160350402. 
[9] 
B. Galperin, H. Nakano, H. Huang and S. Sukoriansky, The ubiquitous zonal jets in the atmospheres of giant planets and Earth oceans,, Geophys. Res. Lett., 31 (2004). 
[10] 
B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki and R. Wordsworth, Anisotropic turbulence and zonal jets in rotating flows with a $\beta$effect,, Nonlinear Processes in Geophysics, 13 (2006), 83. 
[11] 
E. GarcýaMelendo and A. SánchezLavega, A study of the stability of Jovian zonal winds from HST images: 19952000,, Icarus, 152 (2001), 316. 
[12] 
H.P. Huang, B. Galperin and S. Sukoriansky, Anisotropic spectra in twodimensional turbulence on the surface of a rotating sphere,, Phys. Fluids, 13 (2001), 225. 
[13] 
N. A. Maximenko, B. Bang and H. Sasaki, Observational evidence of alternating jets in the world ocean,, Geophys. Res. Lett., 32 (2005). 
[14] 
, NASA/JPL/University of Arizona,, , (). 
[15] 
Sergiu Klainerman and Andrew Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,, Comm. Pure Appl. Math., 34 (1981), 481. doi: 10.1002/cpa.3160340405. 
[16] 
H.O. Kreiss, Problems with different time scales for partial differential equations,, Comm. Pure Appl. Math., 33 (1980), 399. doi: 10.1002/cpa.3160330310. 
[17] 
T. Nozawa and S. Yoden, Formation of zonal band structure in forced twodimensional turbulence on a rotating sphere,, Phys. Fluids, 9 (1997), 2081. doi: 10.1063/1.869327. 
[18] 
C. Porco, et al., Cassini imaging of Jupiter atmosphere, satellites and rings,, Science, 299 (2003), 1541. 
[19] 
G. Roden, Upper ocean thermohaline, oxygen, nutrients, and flow structure near the date line in the summer of 1993,, J. Geophys. Res., 103 (1998), 12919. 
[20] 
G. Roden, Flow and water property structures between the Bering Sea and Fiji in the summer of 1993,, J. Geophys. Res., 105 (2000), 28595. 
[21] 
S. Sukoriansky, B. Galperin and N. Dikovskaya, Universal spectrum of twodimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets,, Phys. Rev. Lett., 89 (2002). 
[22] 
G. Vallis and M. Maltrud, Generation of mean flows and jets on a beta plane and over topography,, J. Phys. Oceanogr., 23 (1993), 1346. 
show all references
References:
[1] 
W. Arendt, C. Batty, M. Hieber and F. Neubrander, "VectorValued Laplace Transforms and Cauchy Problems,", Monographs in Mathematics, 96 (2001). 
[2] 
A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3D Euler and NavierStokes equations for uniformly rotating fluids,, European J. Mechanics B Fluids, 15 (1996), 291. 
[3] 
A. Babin, A. Mahalov and B. Nicolaenko, Global splitting and regularity of rotating shallowwater equations,, European J. Mech. B Fluids, 16 (1997), 725. 
[4] 
H. Beirão da Veiga, On the barotropic motion of compressible perfect fluids,, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 8 (1981), 317. 
[5] 
Bin Cheng, Singular limits and convergence rates of compressible Euler and rotating shallow water equations,, SIAM J. on Mathematical Analysis, 44 (2012), 1050. doi: 10.1137/11085147X. 
[6] 
Bin Cheng and Alex Mahalov, Euler equations on a fast rotating spheretimeaverages and zonal flows,, European J. Mech.  B/Fluids, 37 (2013), 48. doi: 10.1016/j.euromechflu.2012.06.001. 
[7] 
D. G. Ebin, The motion of slightly compressible fluids viewed as a motion with strong constraining force,, Ann. of Math. (2), 105 (1977), 141. 
[8] 
David G. Ebin, Motion of slightly compressible fluids in a bounded domain. I., Comm. Pure Appl. Math., 35 (1982), 451. doi: 10.1002/cpa.3160350402. 
[9] 
B. Galperin, H. Nakano, H. Huang and S. Sukoriansky, The ubiquitous zonal jets in the atmospheres of giant planets and Earth oceans,, Geophys. Res. Lett., 31 (2004). 
[10] 
B. Galperin, S. Sukoriansky, N. Dikovskaya, P. L. Read, Y. H. Yamazaki and R. Wordsworth, Anisotropic turbulence and zonal jets in rotating flows with a $\beta$effect,, Nonlinear Processes in Geophysics, 13 (2006), 83. 
[11] 
E. GarcýaMelendo and A. SánchezLavega, A study of the stability of Jovian zonal winds from HST images: 19952000,, Icarus, 152 (2001), 316. 
[12] 
H.P. Huang, B. Galperin and S. Sukoriansky, Anisotropic spectra in twodimensional turbulence on the surface of a rotating sphere,, Phys. Fluids, 13 (2001), 225. 
[13] 
N. A. Maximenko, B. Bang and H. Sasaki, Observational evidence of alternating jets in the world ocean,, Geophys. Res. Lett., 32 (2005). 
[14] 
, NASA/JPL/University of Arizona,, , (). 
[15] 
Sergiu Klainerman and Andrew Majda, Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids,, Comm. Pure Appl. Math., 34 (1981), 481. doi: 10.1002/cpa.3160340405. 
[16] 
H.O. Kreiss, Problems with different time scales for partial differential equations,, Comm. Pure Appl. Math., 33 (1980), 399. doi: 10.1002/cpa.3160330310. 
[17] 
T. Nozawa and S. Yoden, Formation of zonal band structure in forced twodimensional turbulence on a rotating sphere,, Phys. Fluids, 9 (1997), 2081. doi: 10.1063/1.869327. 
[18] 
C. Porco, et al., Cassini imaging of Jupiter atmosphere, satellites and rings,, Science, 299 (2003), 1541. 
[19] 
G. Roden, Upper ocean thermohaline, oxygen, nutrients, and flow structure near the date line in the summer of 1993,, J. Geophys. Res., 103 (1998), 12919. 
[20] 
G. Roden, Flow and water property structures between the Bering Sea and Fiji in the summer of 1993,, J. Geophys. Res., 105 (2000), 28595. 
[21] 
S. Sukoriansky, B. Galperin and N. Dikovskaya, Universal spectrum of twodimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets,, Phys. Rev. Lett., 89 (2002). 
[22] 
G. Vallis and M. Maltrud, Generation of mean flows and jets on a beta plane and over topography,, J. Phys. Oceanogr., 23 (1993), 1346. 
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