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

• Autorzy: Dalibor Pražák , Josef Žabenský
• 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.

Słowa kluczowe

EN

Ladyzhenskaya fluid; Exponential attractor; Fractal dimension; Lyapunov exponents

Kategorie tematyczne

• 37L30: Attractors and their dimensions, Lyapunov exponents
• 35Q35: PDEs in connection with fluid mechanics
• 76A05: Non-Newtonian fluids

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 7
• Strony: 1264-1282

Daty

wydano

2013-07-01

online

2013-04-26

Twórcy

autor

Dalibor Pražák

• Department of Mathematical Analysis, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

autor

Josef Žabenský

• Department of Mathematical Analysis, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

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

Identyfikatory

DOI

10.2478/s11533-013-0242-8