On backward-time behaviour of Burgers' original model for turbulence

Nonlinearity

Volumn 16, Issue 6, 2003, Pages 1945-1965

  Dascaliuc, Radu ^a  

^a TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242510854     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/16/6/304     Document Type: Article

References (20)

1. [BT73] Bardos C and Tartar L 1973 Sur l'unicité rétrograde des équations parabolique et queliques questiones voisines Arch. Rat. Mech. 50 10-25
2. [Bur39] Burgers J M 1939 Mathematical examples illustrating relations occuring in the theory of turbulent fluid motion Verhandel. Kon. Nederl. Akad. Wetenschappen Amsterdam 17 1-53
3. [Bur40] Burgers J M 1940 Application of a model system to illustrate some points of the statistical theory of free turbulence Proc. Acad. Sci. Amsterdam 43 1-12
4. [Bur48] Burgers J M 1948 A mathematical model illustrating the theory of turbulence Advances in Applied Mechanics vol 1 (New York: Academic)
5. [CFKM97] Constantin P, Foias C, Kukavica I and Majda A 1997 Dirichlet quotients and 2-D periodic Navier-Stokes equations J. Math. Pure Appl. 76 125-53
6. [Ede90] Eden A 1990 On Burgers original model of turbulence Nonlinearity 3 557-66
7. [EFNT94] Eden A, Foias C, Nicolaenko B and Temam R 1994 Exponential attractors for dissipative evolution equations Research in Applied Mathematics vol 37 (Paris: Masson-Wiley)
8. [FJK96] Foias C, Jolly M S and Kukavica I 1996 Localization of attractors by their analytic properties Nonlinearity 9 1565-81
9. [FJL02] Foias C, Jolly M and Lee W-S 2002 Nevanlinna-Pick interpolation of global attractors Nonlinearity 15 1881-904
10. [FT89] Foias C and Temam R 1989 Gevrey class regularity for the solutions of the Navier-Stokes equations J. Funct. Anal. 87 359-69
11. [Hal88] Hale J K 1988 Asymptotic behavior of dissipative systems Mathematical Surveys and Monographs vol 25 (AMS)
12. [IO94] Ishimura N and Ohnishi I 1994 Inertial manifolds for Burgers' original model of turbulence Appl. Math. Lett. 7 33-7
13. [Jol02] Jolly M S 2002 Bifurcation diagrams for the original Burgers' model for turbulence Private communication
14. [Kuk92] Kukavica I 1992 On the behavior of the solutions of the Kuramoto-Sivashinsky equations for negative time J. Math. Anal. Appl. 166 601-6
15. [KM03] Kukavica I and Malcok M 2003 Backward behavior of solutions of the Kuramoto-Sivashinsky equation, submitted
16. [SY02] Sell G R and You Y 2002 Dynamics of evolutionary equations Applied Mathematical Sciences vol 68 (Berlin: Springer)
17. [Tem97] Temam R 1997 Infinite-dimensional dynamical systems in mechanics and physics Applied Mathematical Sciences vol 143 (Berlin: Springer)
18. [Tit03] Titi E 2003 Backward in time blow up of the Forsyth-Burgers equation Private communication
19. [Vuk02a] Vukadinovic J 2002 On the backward behavior of the solutions of the 2D periodic viscous Kamassa-Holm equations J. Dynam. Diff. Eqns 14
20. [Vuk02b] Vukadinovic J 2002 On the backwards behavior of the solutions of the Kelvin filtered 2D periodic Navier-Stokes equations PhD Thesis Indiana University