On global attractors of the 3D Navier-Stokes equations

Journal of Differential Equations

Volumn 231, Issue 2, 2006, Pages 714-754

  Cheskidov, A ^a   Foias, C ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Blow up in finite time; Global attractor; Navier Stokes equations

Indexed keywords

EID: 33749606059     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2006.08.021     Document Type: Article

References (23)

1. Ball J.M. Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations. J. Nonlinear Sci. 7 (1997) 475-502
2. Ball J.M. J. Nonlinear Sci. 8 (1998) 233 Erratum
3. Caraballo T., Marn-Rubio P., and Robinson J.C. A comparison between two theories for multi-valued semiflows and their asymptotic behavior. Set-Valued Anal. 11 (2003) 297-322
4. Chepyzhov V.V., and Vishik M.I. Attractors for Equations of Mathematical Physics. Amer. Math. Soc. Colloq. Publ. vol. 49 (2002), American Mathematical Society, Providence, RI
5. A. Cheskidov, Blow-up in finite time for the dyadic model of the Navier-Stokes equations, Trans. Amer. Math. Soc., in press
6. Constantin P., and Foias C. Navier-Stokes Equation (1989), University of Chicago Press, Chicago
7. Flandoli F., and Schmalfuß B. Weak solutions and attractors for three-dimensional Navier-Stokes equations with nonregular force. J. Dynam. Differential Equations 11 (1999) 355-398
8. Foias C., Manley O.P., Rosa R., and Temam R. Navier-Stokes Equation and Turbulence. Encyclopedia of Mathematics and its Applications vol. 83 (2001), Cambridge University Press, Cambridge
9. Foias C., and Temam R. The connection between the Navier-Stokes equations, and turbulence theory. Directions in Partial Differential Equations (1985), Publ. Math. Res. Center Univ. Wisconsin, Madison, WI 55-73
10. Friedlander S., and Pavlović N. Blowup in a three-dimensional vector model for the Euler equations. Comm. Pure Appl. Math. 57 (2004) 705-725
11. Hale J.K. Asymptotic Behavior of Dissipative Systems (1988), American Mathematical Society, Providence, RI
12. Hale J.K., LaSalle J.P., and Slemrod M. Theory of a general class of dissipative processes. J. Math. Anal. Appl. 39 (1972) 177-191
13. Kukavica I. Role of the pressure for validity of the energy equality for solutions of the Navier-Stokes equation. J. Dynam. Differential Equations 18 (2006) 461-482
14. Katz N.H., and Pavlović N. Finite time blow-up for a dyadic model of the Euler equations. Trans. Amer. Math. Soc. 357 (2005) 695-708
15. Ladyzhenskaya O.A. On the dynamical system generated by the Navier-Stokes equations. J. Sov. Math. 3 (1975) 458-479
16. Ladyzhenskaya O.A. Attractors for Semigroups and Evolution Equations (1991), Cambridge University Press, Cambridge
17. Melnik V.S., and Valero J. On attractors of multivalued semi-flows and differential inclusions. Set-Valued Anal. 6 (1998) 83-111
18. Raugel G., and Sell G.R. Navier-Stokes equations on thin 3D domains, I: Global attractors and global regularity of solutions. J. Amer. Math. Soc. 6 (1993) 503-568
19. R.M.S. Rosa, Asymptotic regularity condition for the strong convergence towards weak limit sets and weak attractors of the 3D Navier-Stokes equations, J. Differential Equations, in press
20. Sell G.R. Global attractors for the three-dimensional Navier-Stokes equations. J. Dynam. Differential Equations 8 (1996) 1-33
21. Sell G.R., and You Y. Dynamics of Evolutionary Equations. Appl. Math. Sci. vol. 143 (2002), Springer-Verlag, New York
22. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Appl. Math. Sci. second ed. vol. 68 (1988), Springer-Verlag, New York
23. Temam R., and Ziane M. Navier-Stokes equations in three-dimensional thin domains with various boundary conditions. Adv. Differential Equations 1 (1996) 499-546