PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2013 | 11 | 7 | 1264-1282
Tytuł artykułu

On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider the so-called Ladyzhenskaya model of incompressible fluid, with an additional artificial smoothing term ɛΔ3. We establish the global existence, uniqueness, and regularity of solutions. Finally, we show that there exists an exponential attractor, whose dimension we estimate in terms of the relevant physical quantities, independently of ɛ > 0.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
7
Strony
1264-1282
Opis fizyczny
Daty
wydano
2013-07-01
online
2013-04-26
Twórcy
  • Department of Mathematical Analysis, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic, prazak@karlin.mff.cuni.cz
  • Department of Mathematical Analysis, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic, josef.zabensky@gmail.com
Bibliografia
  • [1] Ball J.M., Continuity properties and global attractors of generalized semiflows and the Navier-Stokes equations, J. Nonlinear Sci., 1997, 7(5), 475–502 http://dx.doi.org/10.1007/s003329900037[Crossref]
  • [2] Bulíček M., Ettwein F., Kaplický P., Pražák D., The dimension of the attractor for the 3D flow of a non-Newtonian fluid, Commun. Pure Appl. Anal., 2009, 8(5), 1503–1520 http://dx.doi.org/10.3934/cpaa.2009.8.1503[WoS][Crossref]
  • [3] Bulíček M., Ettwein F., Kaplický P., Pražák D., On uniqueness and time regularity of flows of power-law like non-Newtonian fluids, Math. Methods Appl. Sci., 2010, 33(16), 1995–2010
  • [4] Constantin P., Foias C., Navier-Stokes Equations, Chicago Lectures in Math., The University of Chicago Press, Chicago, 1988
  • [5] Feireisl E., Pražák D., Asymptotic Behavior of Dynamical Systems in Fluid Mechanics, AIMS Ser. Appl. Math., 4, American Institute of Mathematical Sciences, Springfield, 2010
  • [6] Ladyzhenskaya O.A., New equations for the description of the motions of viscous incompressible fluids, and global solvability for their boundary value problems, Proc. Steklov Inst. Math., 1967, 102, 95–118
  • [7] Lions J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969
  • [8] Málek J., Nečas J., Rokyta M., Růžička M., Weak and Measure-Valued Solutions to Evolutionary PDEs, Appl. Math. Math. Comput., 13, Chapman & Hall, London, 1996
  • [9] de Rham G., Variétés Différentiables, 3rd ed., Publications de l’Institut de mathématique de l’Université de Nancago, 3, Hermann, Paris, 1973
  • [10] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Appl. Math. Sci., 68, Springer, New York, 1997 [Crossref]
  • [11] Temam R., Navier-Stokes Equations, American Mathematical Society Chelsea, Providence, 2001
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0242-8
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.