Stochastic Navier-Stokes equation and renormalization group theory

Physica D: Nonlinear Phenomena

Volumn 173, Issue 3-4, 2002, Pages 137-152

  Blömker, Dirk ^a   Gugg, Christoph ^b   Maier Paape, Stanislaus ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Galerkin approximation; Renormalization group theory; Stochastic Navier Stokes equation; White noise

Indexed keywords

BOUNDARY CONDITIONS; GALERKIN METHODS; GAUSSIAN NOISE (ELECTRONIC); STOCHASTIC PROGRAMMING; WHITE NOISE;

RENORMALIZATION GROUP (RNG) THEORY;

NAVIER STOKES EQUATIONS;

EID: 0037114542     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(02)00621-8     Document Type: Article

References (17)

1. D. Blömker, S. Maier-Paape, G. Schneider, The stochastic Landau equation as an amplitude equation, Disc. Cont. Dyn. Syst. Series B 1 (4) (2001) 527-541.
2. Checklov A., Yakhot V., Kolmogorov turbulence in a random-force-driven Burgers equation. Phys. Rev. E. 51(4):1995;2739-2742.
3. Checklov A., Yakhot V., Kolmogorov turbulence in a random-force-driven Burgers equation: anomalous scaling and probability density functions. Phys. Rev. E. 52(5):1995;5681-5684.
4. Chen L.-Y., Goldenfeld N., Oono Y., Renormalization group theory for global asymptotic analysis. Phys. Rev. Lett. 73:1994;1311-1315.
5. Chen L.-Y., Goldenfeld N., Oono Y., The renormalization group and singular perturbations: multiple scales, boundary layers and reductive perturbation theory. Phys. Rev. E. 54:1997;376-394.
6. Forster D., Nelson D., Stephen M., Large distance and long time properties of a randomly stirred field. Phys. Rev. A. 16:1977;732-749.
7. C. Gugg, Approximation of stochastic partial differential equations and turbulence in fluids, Ph.D. Thesis, Universität Augsburg, 2001.
8. C. Gugg, H. Kielhöfer, M. Niggemann, On the approximation of the stochastic Burgers equation, Comm. Math. Phys. 230 (1) (2002) 181-199.
9. Matsuba K., Nozaki K., Derivation of amplitude equations by the renormalization group method. Phys. Rev. E. 56:1997;4926-4927.
10. Moise I., Temam R., Renormalization group method. Application to Navier-Stokes equation. Disc. Cont. Dyn. Syst. 6(1):2000;191-210.
11. Moise I., Ziane M., Renormalization group method. Application to partial differential equations. J. Dyn. Diff. Equat. 13:2001;275-321.
12. G. da Prato, J. Zabczyk, Stochastic equations in infinite dimensions, in: Encyclopedia of Mathematics and its Applications, vol. 44, Cambridge University Press, Cambridge, 1992.
13. G. da Prato, J. Zabczyk, Ergodicity for infinite dimensional systems, in: London Mathematical Society Lecture Note Series, vol. 229, Cambridge University Press, Cambridge, 1996.
14. Sasa S., Renormalization group derivation of phase equations. Physica D. 108:1997;45-59.
15. R. Temam, Navier-Stokes equations and nonlinear functional analysis, in: CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 66, 2nd ed., Society for Industrial and Applied Mathematics, 1995.
16. Yakhot V., Orszag S., Renormalization group (RNG) methods for turbulence closure. J. Sci. Comput. 1:1986;3-52.
17. Ziane M., On a certain renormalization group method. J. Math. Phys. 41:2000;3290-3299.