Simple systems with anomalous dissipation and energy cascade

Communications in Mathematical Physics

Volumn 276, Issue 1, 2007, Pages 189-220

  Mattingly, Jonathan C ^a   Suidan, Toufic ^b   Vanden Eijnden, Eric ^c  

^a DUKE UNIVERSITY   (United States)

^b University of California Santa Cruz   (United States)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848825911     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-007-0333-0     Document Type: Article

References (14)

1. Cheskidov, A., Friedlander, S., Pavlović, N.: An Inviscid Dyadic Model of Turbulence: The Global Attractor. arXiv:math.AP/06108115 v1, 2006
2. Cheskidov, A., Friedlander, S., Pavlović, N.: An Inviscid Dyadic Model of Turbulence: The Fixed Point and Onsager's Conjecture. http://arxiv.org/list/math.AP/0610814, 2006
3. Constantin P., E W. and Titi E.S. (1994). Onsager's conjecture on the energy conservation for solutions of Euler's equation. Commun. Math. Phys. 165(1): 207-209
4. 2. http://arxiv.org/list/math.AP/0611782 v1, 2006
5. Duchon J. and Robert R. (2000). Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations. Nonlinearity 13(1): 249-255
6. E, W.: Stochastic hydrodynamics. In: Current developments in mathematics, 2000, Somerville, MA: Int. Press, 2001, pp. 109-147
7. Eyink G.L. (2001). Dissipation in turbulent solutions of 2D Euler equations. Nonlinearity 14(4): 787-802
8. Feller W. (1954). The general diffusion operator and positivity preserving semi-groups in one dimension. Ann. of Math. (2) 60: 417-436
9. Falkovich G., Gawȩdzki K. and Vergassola M. (2001). Particles and fields in fluid turbulence. Rev. Mod. Phys. 73(4): 913-975
10. Flajolet P. and Odlyzko A. (1990). Singularity analysis of generating functions. SIAM J. Discrete Math. 3(2): 216-240
11. Frisch, U.: Turbulence. Cambridge: Cambridge University Press, 1995
12. Hilberdink T. (2001). A Tauberian theorem for power series. Arch. Math. (Basel) 77(4): 354-359
13. McKean H.P. (1956). Elementary solutions for certain parabolic partial differential equations. Trans. Amer. Math. Soc. 82: 519-548
14. Srinivasan, R.: Simple models with cascade of energy and anomalous dissipation. In: Oliver Buhler, Charles Doering, ed. Fast times and fine scales, Woods Hole Oceanographic Institution Technical Reports. Woods Hole Oceanographic Institution, 2005