Unique strong solutions and V-attractors of a three dimensional system of globally modified Navier-Stokes equations

Advanced Nonlinear Studies

Volumn 6, Issue 3, 2006, Pages 411-436

  Caraballo, Tomás ^a   Real, José ^a   Kloeden, Peter E ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

3 dimensional Navier Stokes equations; Bounded entire weak solutions; Existence and uniqueness of strong solutions; Flattening property; Galerkin approximations; Global attractors; Weak solutions

Indexed keywords

EID: 33749373629     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2006-0304     Document Type: Article

References (12)

1. P. Constantin, Near Identity Transformations For the Navier-Stokes Equations, Handbook of Mathematical Fluid Dynamics, Vol. II, 117-141, North-Holland, Amsterdam, 2003.
2. P. Constantin and C. Foias, Navier-Stokes equations, Chicago Lectures in Mathematics. University of Chicago Press, Chicago, 1988.
3. F. Flandoli and B. Maslowski, Ergodicity of the 2-D Navier-Stokes Equation under random perturbations, Commun. Math. Phys. 171 (1995), 119-141.
4. A.V. Kapustyan and J. Valero, Global continuous solutions, uniqueness and attractors for the 3-D Navier-Stokes system, preprint, 2005.
5. P.E. Kloeden, Pullback attractors of nonautonomous semidynamical systems, Stochastics & Dynamics 3, No. 1, (2003), 101-112.
6. P.E. Kloeden and J.A. Langa, Flattening, squeezing and the existence of random attractors, Proc. Roy. Soc. London (to appear).
7. J.L. Lions.Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.
8. Qingfeng Ma, Shouhong Wang and Chenkui Zhong, Necessary and sufficient conditions for the existence of global attractors for semigroups and applications, Indiana Univ. Math. J. 51 (2002), 1541-1559.
9. J.C. Robinson, Infinite-dimensional dynamical systems, Cambridge University Press, Cambridge, 2001.
10. R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1977.
11. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis, Second Edition, SIAM, Philadelphia, 1995.
12. M. Wiegner, The Navier-Stokes equations - a never ending challenge, Jber. d. Dt. Math.-Verein. 101 (1999), 1-25.