On global attractors of the 3D Navier-Stokes equations

@article{Cheskidov2006OnGA,
  title={On global attractors of the 3D Navier-Stokes equations},
  author={A. Cheskidov and C. Foiaș},
  journal={Journal of Differential Equations},
  year={2006},
  volume={231},
  pages={714-754}
}
  • A. Cheskidov, C. Foiaș
  • Published 2006
  • Mathematics
  • Journal of Differential Equations
  • Abstract In view of the possibility that the 3D Navier–Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with respect to two topologies—weak and strong. Each such system possesses a global attractor in the weak topology, but not necessarily in the strong. In case the latter exists and is weakly closed, it coincides with the weak global attractor. We give a… CONTINUE READING
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    References

    SHOWING 1-10 OF 22 REFERENCES
    Blow-up in finite time for the dyadic model of the Navier-Stokes equations
    • 53
    • PDF
    Global attractors for the three-dimensional Navier-Stokes equations
    • 203
    Erratum to: Continuity Properties and Global Attractors of Generalized Semiflows and the Navier-Stokes Equations
    • 182
    • Highly Influential
    • PDF
    Navier-Stokes equations in three-dimensional thin domains with various boundary conditions
    • 124
    • PDF
    Asymptotic Behavior of Dissipative Systems
    • 2,232
    • PDF
    Blowup in a three-dimensional vector model for the Euler equations
    • 43
    • PDF
    GLOBAL ATTRACTORS FOR DAMPED SEMILINEAR WAVE EQUATIONS
    • 305
    • PDF
    Theory of a general class of dissipative processes.
    • 57