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

Dalibor Pražák; Josef Žabenský

Open Mathematics (2013)

  • Volume: 11, Issue: 7, page 1264-1282
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dalibor Pražák, and Josef Žabenský. "On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model." Open Mathematics 11.7 (2013): 1264-1282. <http://eudml.org/doc/269498>.

@article{DaliborPražák2013,
abstract = {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.},
author = {Dalibor Pražák, Josef Žabenský},
journal = {Open Mathematics},
keywords = {Ladyzhenskaya fluid; Exponential attractor; Fractal dimension; Lyapunov exponents; exponential attractor; fractal dimension},
language = {eng},
number = {7},
pages = {1264-1282},
title = {On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model},
url = {http://eudml.org/doc/269498},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Dalibor Pražák
AU - Josef Žabenský
TI - On the dimension of the attractor for a perturbed 3d Ladyzhenskaya model
JO - Open Mathematics
PY - 2013
VL - 11
IS - 7
SP - 1264
EP - 1282
AB - 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.
LA - eng
KW - Ladyzhenskaya fluid; Exponential attractor; Fractal dimension; Lyapunov exponents; exponential attractor; fractal dimension
UR - http://eudml.org/doc/269498
ER -

References

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  3. [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 Zbl1202.35152
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  6. [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. [7] Lions J.-L., Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires, Dunod, Gauthier-Villars, Paris, 1969 
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  9. [9] de Rham G., Variétés Différentiables, 3rd ed., Publications de l’Institut de mathématique de l’Université de Nancago, 3, Hermann, Paris, 1973 
  10. [10] Temam R., Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Appl. Math. Sci., 68, Springer, New York, 1997 [Crossref] Zbl0871.35001
  11. [11] Temam R., Navier-Stokes Equations, American Mathematical Society Chelsea, Providence, 2001 

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