Global φ-attractor for a modified 3D Bénard system on channel-like domains

O.V. Kapustyan; A.V. Pankov

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, page 1-9, electronic only
  • ISSN: 2353-0626

Abstract

top
In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.

How to cite

top

O.V. Kapustyan, and A.V. Pankov. "Global φ-attractor for a modified 3D Bénard system on channel-like domains." Nonautonomous Dynamical Systems 1 (2014): 1-9, electronic only. <http://eudml.org/doc/266645>.

@article{O2014,
abstract = {In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.},
author = {O.V. Kapustyan, A.V. Pankov},
journal = {Nonautonomous Dynamical Systems},
keywords = {Three-dimensional Bénard problem; three-dimensional; Navier-Stokes equations; multi-valued nonautonomous dynamicalsystem; global attractor; unbounded domain; three-dimensional Bénard problem; three-dimensional Navier-Stokes equations; multi-valued nonautonomous dynamical system},
language = {eng},
pages = {1-9, electronic only},
title = {Global φ-attractor for a modified 3D Bénard system on channel-like domains},
url = {http://eudml.org/doc/266645},
volume = {1},
year = {2014},
}

TY - JOUR
AU - O.V. Kapustyan
AU - A.V. Pankov
TI - Global φ-attractor for a modified 3D Bénard system on channel-like domains
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
SP - 1
EP - 9, electronic only
AB - In this paper we prove the existence of a global φ-attractor in the weak topology of the natural phase space for the family of multi-valued processes generated by solutions of a nonautonomous modified 3D Bénard system in unbounded domains for which Poincaré inequality takes place.
LA - eng
KW - Three-dimensional Bénard problem; three-dimensional; Navier-Stokes equations; multi-valued nonautonomous dynamicalsystem; global attractor; unbounded domain; three-dimensional Bénard problem; three-dimensional Navier-Stokes equations; multi-valued nonautonomous dynamical system
UR - http://eudml.org/doc/266645
ER -

References

top
  1. [1] J. Ball, Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations, in "Mechanics: from theory to computation", Springer, New York, 2000, p. 447-474. Zbl0958.35101
  2. [2] M. Cabral, R. Rosa, R. Temam, Existence and dimension of the attractor for the Bénard problem on channel-like domain, Discrete Contin. Dyn. Syst., 10 (2004), 89-116. Zbl1049.37046
  3. [3] T. Caraballo, P.E. Kloeden, J. Real, Unique strong solution and V-attractor of three-dimensional system of globally modified Navier-Stokes equation, Advanced Nonlinear Studies, 6 (2006), 411-436. Zbl1220.35115
  4. [4] V.V. Chepyzhov, M.I. Vishik, Evolution equations and their trajectory attractors, J. Math. Pures Appl. 76 (1997), 913-964. Zbl0896.35032
  5. [5] C. Foias, R. Temam, The connection between the Navier-Stokes equations, dynamical systems, and turbulence theory, in "Directions in Partial Differential Equations", Academic Press, 1987, p.55-73. 
  6. [6] O.A. Ladyzhenskaya, "Attractors of semigroups and evolution equations", Cambridge University Press, Cambridge, 1991. Zbl0755.47049
  7. [7] J.L. Lions, "Quelques méthodes de résolutions des problèmes aux limites non linéaires", Dunod, Gauthier-Villars, Paris, 1969. Zbl0189.40603
  8. [8] O.V. Kapustyan, V.S. Melnik, J. Valero, A weak attractors and properties of solutions for the three-dimensional Bénard problem, Discrete Contin. Dyn. Syst., 18 (2007), 449-481. Zbl1143.35013
  9. [9] O.V. Kapustyan, A.V. Pankov, J. Valero, On global attractors of multivalued semiflows generated by the 3D Bénard system, Set-Valued and Variat. Anal., 20 (2012), 445-465. [WoS] Zbl1259.35042
  10. [10] O.V. Kapustyan, J. Valero, Weak and strong attractors for the 3D Navier-Stokes system, J. Differential Equations, 240 (2007), 249-278. Zbl1131.35056
  11. [11] P.E. Kloeden, J. Valero, The Kneser property of the weak solutions of the three-dimensional Navier-Stokes equations, Discrete Contin. Dyn. Syst., 28 (2010), 161-179. Zbl1194.35061
  12. [12] V.S. Melnik, J. Valero, On attractors of multi-valued semi-flows and differential inclusions, Set-Valued Anal. 6 (1998), 83-111. 
  13. [13] D.E. Norman, Chemically reacting fluid flows: weak solutions and global attractors, J. Differential Equations, 152 (1999), 75-135. Zbl0936.35133
  14. [14] J. Robinson, "Infinite-dimensional dynamical systems", Cambridge University Press, Cambridge, 2001. Zbl1026.37500
  15. [15] M. Romito, The uniqueness of weak solutions of the globally modified Navier-Stokes equations, Advanced Nonlinear Studies, 9 (2009), 425-427. Zbl1181.35178
  16. [16] R. Rosa, The global attractor for the 2D Navier-Stokes flow on some unbounded domain, Nonlinear Anal., 32 (1998), 71-85. Zbl0901.35070
  17. [17] G. Sell, Global attractors for the three-dimensional Navier-Stokes equations, J. Dynamics Differential Equations 8 (1996), 1-33. Zbl0855.35100
  18. [18] G.R. Sell, Y. You, "Dynamics of evolutionary equations", Springer, New-York, 2002. Zbl1254.37002
  19. [19] J. Simon, "Compact sets in the space Lp(0; T ;B)", Ann. Mat. Pura Appl. 146 (1986), 65-96. Zbl0629.46031
  20. [20] J. Simsen, C. Gentile, On attractors for multivalued semigroups defined by generalized semiflows, Set-Valued Anal., 16 (2008), 105-124. [WoS] Zbl1143.35310
  21. [21] R. Temam, "Navier-Stokes equations", North-Holland, Amsterdam, 1979. Zbl0426.35003
  22. [22] R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics", Springer-Verlag, New York, 1988. Zbl0662.35001
  23. [23] M.Z.Zgurovsky, P.O. Kasyanov, O.V. Kapustyan, J. Valero, N.V. Zadoinchuk, "Evolution inclusions and variational inequalities for Earth data processing III", Springer-Verlag, New York, 2012. Zbl1317.86003

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.