Local existence for the FENE-dumbbell model of polymeric fluids

Archive for Rational Mechanics and Analysis

Volumn 181, Issue 2, 2006, Pages 373-400

  Zhang, Hui ^a   Zhang, Pingwen ^b  

^a BEIJING NORMAL UNIVERSITY   (China)

^b PEKING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646894129     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-006-0416-7     Document Type: Article

References (17)

1. BARRETT J.W., SCHWAB C., SÜLI E.: Existence of global weak solutions for sone polymeric flow models, preprint
2. BIRD R.B., ARMSTRONG R.C., HASSAGER O.: Dynamics of Polymeric Liquids, 2nd Edn., Vol 1 & 2. John Wiley, New York, 1987
3. CHAUVIÈRE C., LOZINSKI A.: Simulation of complex viscoelastic flows using Fokker-Planck equation: 3D FENE model. Submitted to J. Non-Newtonian Fluid Mech.
4. DOI M., EDWARDS S.F.: The Theory of Polymer Dynamics. Oxford University Press, Oxford, 1986
5. DU QIANG., LIU CHUN., YU PENG.: FENE dumbbell model and its several linear and nonlinear closure approximations. Multiscale Model. Simul. In press
6. E.W., LI T., ZHANG P.: Convergence of a stochastic method for the modeling of polymeric fluids. Acta Math Appl Sin. Eng. Ser. 18, 529-536 (2002)
7. LI E. W., T., ZHANG P.: Well-Posedness for the dumbbell model of polymeric fluids. Comm. Math. Phys. 248, 409-427 (2003)
8. JOURDAIN B., LELIEVRET., LE BRIS C.: Numerical analysis of micro-macro simulations of polymeric fluid flows: a simple case. Math. Models Methods App. Sci. 12, 1205-1243 (2002)
9. JOURDAIN B., LELIEVRE T., LE BRIS C.: Existence of solution for a micro-macro model of polymeric fluid: the FENE model. J. Funct. Anal. 209. 162-193 (2004)
10. JOURDAIN B., LELIEVRE T.: Mathematical analysis of a stochastic differential equation arising in the micro-macro modelling of polymeric fluids. Preprint, CERMICS 2002-225
11. KRÖGER M.: Simple models for complex nonequilibrium fluids. Phys. Rep. 390, 451-551 (2004)
12. LIN F.H., LIU C., ZHANG P.: On a micro-macro model for polymeric fluids near equilibrium. Preprint
13. LI T.J., ZHANG H., ZHANG P.W.: Local existence for the dumbbell model of polymeric fluids. Comm. Partial Differential Equations 29, 903-923 (2004)
14. LOZINSKI A., CHAUVIÈRE C.: A fast solver for Fokker-Planck equation applied to viscoelastic flows calculations: 2D FENE model. J. Comp. Phys. 189, 607-625 (2003)
15. PRAVIA J.: Numerical methods for viscoelastic fluids. Doctoral Thesis, 2002
16. RENARDY M.: Local existence of solutions of the Dirichlet initial boundary problem for incompressible hypoelastic materials. SIAM J. Math. Anal. 21, 1369-1385 (1990)
17. RENARDY M.: An existence theorem for model equations resulting from kinetic theories, SIAM J. Math. Anal. 22, 313-327 (1991)