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3 - A continuous model for turbulent energy cascade

Published online by Cambridge University Press:  05 November 2012

A. Cheskidov
Affiliation:
University of Illinois
R. Shvydkoy
Affiliation:
University of Chicago
S. Friedlander
Affiliation:
University of Southern California
James C. Robinson
Affiliation:
University of Warwick
José L. Rodrigo
Affiliation:
University of Warwick
Witold Sadowski
Affiliation:
Uniwersytet Warszawski, Poland
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Publisher: Cambridge University Press
Print publication year: 2012

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References

Bhat, S. & Fetecau, R.C. (2006) A Hamiltonian regularization of the Burgers equation. J. Nonlinear Sci. 16, no. 6, 615–638.Google Scholar
Cheskidov, A. & Friedlander, S. (2009) The vanishing viscosity limit for a dyadic model. Phys.D 238, no. 8, 783–78.Google Scholar
Cheskidov, A., Constantin, P., Friedlander, S., & Shvydkoy, R. (2008) Energy conservation and Onsager's conjecture for the Euler equations. Nonlinearity 21, no. 6, 1233–1252.Google Scholar
Constantin, P., E, W., , & Titi, E.S. (1994) Onsager's conjecture on the energy conservation for solutions of Euler's equation. Comm. Math. Phys. 165, no. 1, 207–209.Google Scholar
De Lellis, C. & Székelyhidi, L., (2009) The Euler equations as a differential inclusion. Ann. of Math. (2) 170, no. 3, 1417–1436.Google Scholar
De Lellis, C. & Székelyhidi, L., (2012) Dissipative Euler flows and Onsager's conjecture. arXiv:1205.2626
Desnyansky, V.N. & Novikov, E.A. (1974) The evolution of turbulence spectra to the similarity regime. Izv. Akad. Nauk SSSR Fiz. Atmos. Okeana 10, 127–136.Google Scholar
Duchon, J. & Robert, R. (2000) Inertial energy dissipation for weak solutions of incompressible Euler and Navier–Stokes equations. Nonlinearity 13, no. 1, 249–255,.Google Scholar
Eyink, G.L. (1994) Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer. Phys.D 78, no. 3–4, 222–240.Google Scholar
Eyink, G.L. (1995) Besov spaces and the multifractal hypothesis. J. Statist. Phys. 78, no. 1–2, 353–375.Google Scholar
Eyink, G.L. & Sreenivasan, R.K. (2006) Onsager and the theory of hydrodynamic turbulence. Rev. Modern Phys. 78, no. 1, 87–135.Google Scholar
Frisch, U. & Parisi, G. (1985) On the singularity structure of fully developed turbulence. In Ghil, M., Benzi, R., & Parisi, G. (eds.) Turbulence and predictability in geophysical fluid dynamics and climate dynamics. Proc. International Summer School of Physics “Enrico Fermi”, Amsterdam, North-Holland, 84–87.
Frisch, U. (1995) Turbulence. Cambridge University Press, Cambridge, England.
Katz, N.H. & Pavlović, N. (2005) Finite time blow-up for a dyadic model of the Euler equations. Trans. Amer. Math. Soc. 357, no. 2, 695–708 (electronic).
Kiselev, A. & Zlatoš, A. (2005) On discrete models of the Euler equation. Int. Math. Res. Not. 38, 2315–2339.Google Scholar
Kolmogorov, A.N. (1941) The local structure of turbulence in incompressible viscous fluids at very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 301–305.Google Scholar
Norgard, G. & Mohseni, K. (2009) On the Convergence of the Convectively Filtered Burgers Equation to the Entropy Solution of the Inviscid Burgers Equation. Multiscale Model. Simul. 7, 1811–1837.Google Scholar
Onsager, L. (1949) Statistical hydrodynamics. Nuovo Cimento (9) 6, Supplemento, 2 (Convegno Internazionale di Meccanica Statistica), 279–287.Google Scholar
Scheffer, V. (1993) An inviscid flow with compact support in space-time. J. Geom. Anal. 3, no. 4, 343–401.Google Scholar
Shnirelman, A. (1997) On the nonuniqueness of weak solution of the Euler equation. Comm. Pure Appl. Math. 50, no. 12, 1261–1286.Google Scholar

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