C. Bardos, What use for the mathematical theory of the Navier-Stokes equations, Mathematical fluid mechanics, pp.1-25, 2001.

G. K. Batchelor, The theory of homogeneous turbulence. Reprint. Cambridge Science Classics, 1982.

P. T. Bateman, On the representations of a number as the sum of three squares, Trans. Amer. Math. Soc, vol.71, pp.70-101, 1951.

H. Bercovici, P. Constantin, C. Foias, and O. P. Manley, Exponential decay of the power spectrum of turbulence, J. Statist. Phys, vol.80, issue.3-4, pp.579-602, 1995.

A. Biryuk and W. Craig, Bounds on Kolmogorov spectra for the Navier-Stokes equations, 2009.

O. N. Boratav and R. B. Pelz, Structures and structure functions in the inertial range of turbulence, Phys. Fluids, vol.9, issue.5, pp.1400-1415, 1997.

V. Borue and S. A. Orszag, Spectra in helical three-dimensional homogeneous isotropic turbulence, Phys. Rev. E, issue.3, pp.7005-7009, 1997.

M. E. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf et al., The Taylor-Green vortex and fully developed turbulence, J. Statist. Phys, vol.34, issue.5-6, pp.1049-1063, 1984.

M. E. Brachet, A primer in classical turbulence theory. Instabilities and nonequilibrium structures, Nonlinear Phenom. Complex Systems, vol.5, pp.5-34, 1995.

M. E. Brachet, Lectures Notes on Turbulence

L. Brandolese, Space-time decay of Navier-Stokes flows invariant under rotations, Math. Ann, vol.329, issue.4, pp.685-706, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00000292

L. Brandolese and F. Vigneron, New asymptotic profiles of nonstationary solutions of the Navier-Stokes system, J. Math. Pures Appl, issue.9, pp.64-86, 2007.

L. Brandolese, Concentration-diffusion effects in viscous incompressible flows, Indiana Univ. Math. J, vol.58, issue.2, pp.789-806, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00269399

L. Caffarelli, R. Kohn, and L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math, vol.35, issue.6, pp.771-831, 1982.

D. Chae, On the a priori estimates for the Euler, the Navier-Stokes and the quasi-geostrophic equations, Adv. Math, vol.221, issue.5, pp.1678-1702, 2009.

F. Chamizo and H. Iwaniec, On the sphere problem, Rev. Mat. Iberoamericana, vol.11, issue.2, pp.417-429, 1995.

J. Chemin, English translation by Isabelle Gallagher and Dragos Iftimie, Oxford Lecture Series in Mathematics and its Applications, vol.14, 1998.

J. Chemin, Le système de Navier-Stokes incompressible soixante dix ans après Jean Leray. (French) Actes des Journées MathématiquesMathématiquesà la Mémoire de Jean Leray, vol.9, pp.99-123, 2004.

J. Chemin, B. Desjardins, I. Gallagher, and E. Grenier, Mathematical geophysics. An introduction to rotating fluids and the Navier-Stokes equations, Oxford Lecture Series in Mathematics and its Applications, vol.32, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00112069

C. Cheverry, Cascade of phases in turbulent flows, Bull. Soc. Math. France, vol.134, issue.1, pp.33-82, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00001175

S. K. Choi, A. V. Kumchev, and R. Osburn, On sums of three squares, Int. J. Number Theory, vol.1, issue.2, pp.161-173, 2005.

P. Constantin, Some mathematical aspects of incompressible fluid mechanics. Partial differential equations and their applications, CRM Proc. Lecture Notes, vol.12, pp.51-69, 1995.

P. Constantin, Q. Nie, and S. Tanveer, Bounds for second order structure functions and energy spectrum in turbulence, The International Conference on Turbulence, vol.11, pp.2251-2256, 1998.

P. Constantin, Euler equations, Navier-Stokes equations and turbulence. Mathematical foundation of turbulent viscous flows, Lecture Notes in Math, pp.1-43, 1871.

P. A. Davidson, Turbulence. An Introduction for Scientists and Engineers, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00147158

J. Duchon and R. Robert, Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations, Nonlinearity, vol.13, issue.1, pp.249-255, 2000.

T. Estermann, On the representations of a number as a sum of three squares, Proc. London Math. Soc, vol.9, issue.3, pp.1959-575

C. Foias and R. Temam, Gevrey class regularity for the solutions of the Navier-Stokes equations, J. Funct. Anal, vol.87, issue.2, pp.359-369, 1989.

C. Foias, O. P. Manley, R. M. Rosa, and R. Temam, Estimates for the energy cascade in three-dimensional turbulent flows, C. R. Acad. Sci. Paris Sér. I Math, vol.333, issue.5, pp.499-504, 2001.

C. Foias, O. P. Manley, R. M. Rosa, and R. Temam, Navier-Stokes equations and turbulence, English summary) Encyclopedia of Mathematics and its Applications, vol.83, 2001.

U. Frisch and . Turbulence, The legacy of A. N. Kolmogorov, 1995.

H. Fujita and T. Kato, On the Navier-Stokes initial value problem, I. Arch. Rational Mech. Anal, vol.16, pp.269-315, 1964.

G. P. Galdi, An introduction to the mathematical theory of the Navier-Stokes equations, Springer Tracts in Natural Philosophy, vol.38, 1994.

Z. Gruji´cgruji´c and I. Kukavica, Space analyticity for the Navier-Stokes and related equations with initial data in L p, J. Funct. Anal, vol.152, issue.2, pp.447-466, 1998.

J. Harlim and A. J. Majda, Mathematical strategies for filtering complex systems: regularly spaced sparse observations, J. Comput. Phys, vol.227, issue.10, pp.5304-5341, 2008.

S. Heinz, On the Kolmogorov constant in stochastic turbulence models, Phys. Fluids, vol.14, issue.11, pp.4095-4098, 2002.

E. Hopf, Statistical hydromechanics and functional calculus, J. Rational Mech. Anal, vol.1, pp.87-123, 1952.

S. Kida and S. A. Orszag, Energy and spectral dynamics in decaying compressible turbulence, J. Sci. Comput, vol.7, issue.1, pp.1-34, 1992.

H. Koch and D. Tataru, Well-posedness for the Navier-Stokes equations, Adv. Math, vol.157, issue.1, pp.22-35, 2001.

A. N. Kolmogorov, English translation by V. Levin in Turbulence and stochastic processes: Kolmogorov's ideas 50 years on, Proc. Roy. Soc. London Ser. A, vol.30, issue.1890, pp.9-13, 1941.

A. N. Kolmogorov, On Degeneration of Isotropic Turbulence in an Incompressible Viscous Liquid, Dokl. Akad. Nauk SSSR, vol.31, pp.538-541, 1941.

A. N. Kolmogorov, English translation by V. Levin. Turbulence and stochastic processes: Kolmogorov's ideas 50 years on, Proc. Roy. Soc. London Ser. A, vol.32, issue.1890, pp.15-17, 1941.

A. N. Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech, vol.13, pp.82-85, 1962.

L. Korson, W. Drost-hansen, and F. J. Millero, Viscosity of water at various temperatures, J. Phys. Chem, vol.73, issue.1, pp.34-39, 1969.

S. B. Kuksin, Spectral properties of solutions for nonlinear PDEs in the turbulent regime, Geom. Funct. Anal, vol.9, issue.1, pp.141-184, 1999.

Y. Le-jan and A. S. Sznitman, Cascades aléatoires etéquationsetéquations de Navier-Stokes, French) C. R. Acad. Sci. Paris Sér. I Math, vol.324, issue.7, pp.823-826, 1997.

P. G. Lemarié-rieusset, Une remarque sur l'analyticité des solutions milds deséquationsdeséquations de Navier-Stokes dans R 3, C. R. Acad. Sci. Paris Sér. I Math, vol.330, issue.3, pp.183-186, 2000.

P. G. Lemarié-rieusset, Recent developments in the Navier-Stokes problem, Chapman & Hall/CRC Research Notes in Mathematics, vol.431, 2002.

P. G. Lemarié-rieusset, Nouvelles remarques sur l'analyticité des solutions milds deséquationsdeséquations de Navier-Stokes dans R 3 . (French), C. R. Math. Acad. Sci. Paris, vol.338, issue.6, pp.443-446, 2004.

J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace. (French) Acta Math, vol.63, pp.193-248, 1934.

M. Lesieur, S. Ossia, and O. Métais, Infrared pressure spectra in two-and three-dimensional isotropic incompressible turbulence, Phys. Fluids, vol.11, issue.6, pp.1535-1543, 1999.

M. Lesieur, Turbulence in fluids. Third edition. Fluid Mechanics and its Applications, vol.40, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00261553

R. Lien and E. A. D'asaro, Measurement of Turbulent Kinetic Energy Dissipation Rate with a Lagrangian Float, J. of Atmospheric and Oceanic Technology, pp.964-976, 2006.

P. Lions, Mathematical topics in fluid mechanics, vol.1, 1996.

K. Masuda, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation, Proc. Japan Acad, vol.43, pp.827-832, 1967.

W. D. Mccomb, The physics of fluid turbulence, Oxford Engineering Science Series, vol.25, 1991.

A. Obukhoff, On the energy distribution in the spectrum of a turbulent flow, Dokl. Akad. Nauk SSSR, vol.32, pp.19-21, 1941.

M. Paicu,

P. Germain, N. Pavlovi´cpavlovi´c, and G. Staffilani, Regularity of solutions to the Navier-Stokes equations evolving from small data in BMO ?1, Int. Math. Res. Not. IMRN, issue.21, 2007.

J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal, vol.9, pp.187-195, 1962.

H. Sohr, The Navier-Stokes equations. An elementary functional analytic approach, 2001.

K. R. Sreenivasan, On the universality of the Kolmogorov constant, Phys. Fluids, vol.7, issue.11, pp.2778-2784, 1995.

K. R. Sreenivasan, Fluid turbulence, Reviews of Modern Physics, vol.71, issue.2, pp.383-395, 1999.

E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, issue.32, 1971.

R. Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, vol.2, 1984.

F. Vigneron, Spatial decay of the velocity field of an incompressible viscous fluid in R d, Nonlinear Anal, vol.63, issue.4, pp.525-549, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00021439

G. S. Welter, A. R. Wittwer, G. A. Degrazia, O. C. Acevedo, O. L. De-moraes et al., Measurements of the Kolmogorov constant from laboratory and geophysical wind data, Physica A, vol.388, pp.3745-3751, 2009.