NONLINEAR FOKKER-PLANCK NAVIER-STOKES SYSTEMS

Communications in Mathematical Sciences

Volumn 3, Issue 4, 2005, Pages 531-544

  Constantin, Peter ^a  

^a UNIVERSITY OF CHICAGO   (United States)

Author keywords

Fokker planck equations; Microscopic inclusions; Navier stokes equations; Smoluchowski equations

Indexed keywords

EID: 33745419628     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2005.v3.n4.a4     Document Type: Article

References (19)

1. [1] J. W. Barrett, C. Schwab and E. Suli, Existence of global weak solutions for some polymeric flow models, Math. Models and Methods in Appl. Science, 15(6), 939-983, 2005.
2. [2] P. Constantin, I. Kevrekidis and E. Titi, Asymptotic states of a Smoluchowski equation, ARMA,174, 365-384, 2004.
3. [3] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, Oxford1988.
4. [4] W. E, T. J. Li and P-W. Zhang, Well-posedness for the dumbell model of polymeric fluids,Commun. Math. Phys., 248, 409-427, 2004.
5. [5] I. Fatkullin and V. Slastikov, A note on the Onsager model of nematic phase transitions,Comm. Math. Sci., 3, 21-26, 2005.
6. [6] G. Forest, Q. Wang and R. Zhou, The weak shear phase diagram for nematic polymers, Rheo-logica Acta, 43, 17-37, 2004.
7. [7] G. Forest, Q. Wang and R. Zhou, The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates, Rheologica Acta 44(1), 80-93, 2004.
8. [8] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic Press, Lon-don 1978.
9. [9] L. Hormander, The Analysis of Linear Partial Differential Operators, Springer-Verlag, Berlin,Heidelberg, New York, Tokyo, 3, 1985.
10. [10] B. Jourdain, T. Lelievre and C. Le Bris, Numerical analysis of micro-macro simulations of polymeric flows: a simple case, Math. Models in Appl. Science, 12, 1205-1243, 2002.
11. [11] B. Jourdain, T. Lelievre and C. Le Bris, Existence of solutions for a micro-macro model of polymeric fluid: the FENE model, preprint, 2005.
12. [12] B. Jourdain, C. Le Bris, T. Lelievre and F. Otto, Long time asymptotics of a multiscale model for polymeric fluid flows, preprint, March 2005.
13. [13] F. Lin, C. Liu and P. Zhang, On a micro-macro model of polymeric fluids near equilibrium, preprint, 2005.
14. [14] C. Luo, H. Zhang and P-W. Zhang, The structure of the equilibrium solutions of one dimen-sional Doi equation, Nonlinearity, 18, 379-389, 2005.
15. [15] H. Liu, H. Zhang and P-W Zhang, Axial symmetry and classification of stationary solutions of Doi-Onsager Equation on the sphere with Maier-Saupe potential, Comm. Math. Sci., 3, 201-218, 2005.
16. [16] T. Li, H. Zhang and P-W. Zhang, Local existence for the dumbell model of polymeric fluids,Commun. PDE, 29, 903-923, 2004.
17. [17] L. Onsager, The effects of shape on the interaction of colloidal particles, Ann. N.Y. Acad. Sci.,51, 627-659, 1949.
18. [18] F. Otto and A. Tzavaras, Continuity of velocity gradients in suspensions of rod-like molecules,SFB, Preprint, 147, 2004.
19. [19] M. Renardy, An existence theorem for model equations resulting from kinetic theories of poly-mer solutions, SIAM J. Math. Analysis, 23, 313-327, 1991.