Well-Posedness for the Dumbbell Model of Polymeric Fluids
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The dumbbell model is a coupled hydrodynamic-kinetic model for polymeric fluids in which the configurations of the dumbbells are described by stochastic differential equations. We prove well-posedness of this model by deriving directly a priori estimates on the stochastic model. Our results can be used to analyze stochastic simulation methods such as the ones that are based on Brownian configuration fields.
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- 1.Bird, R.B., Curtiss, C.F., Armstrong, R.C., Hassager, O.: Dynamics of Polymeric Liquids, Vol. 2: Kinetic Theory. New York: John Wiley, 1987Google Scholar
- 2.Doi, M., Edwards, S.F.: The theory of polymer dynamics. Oxford: Oxford University Press, 1986Google Scholar
- 3.E, W., Li, T., Zhang, P.: Convergence of a stochastic method for the modeling of polymeric fluids. Acta Mathematicae Applicatae Sinica, English Series, 18(4), 529–536 (2002)Google Scholar
- 4.E, W., Li, T., Zhang, P.: Convergence analysis of BCF methods. In preparationGoogle Scholar
- 9.Karatzas, I., Shreve, S.E.: Brownian motion and stochastic calculus (2nd edition), New York: Springer-Verlag, 1991Google Scholar
- 11.Li, T., Zhang, H., Zhang, P.: Local existence for the dumbbell model of polymeric fluids. Comm. PDE 29, 903–923 (2004)Google Scholar
- 12.Li, T., Zhang, P., Zhou, X.: Well-posedness and numerical analysis of stochastic models for liquid crystal polymers. Submitted to Comm. Math. Sci.Google Scholar
- 14.Majda, A.J.: Compressible fluid flow and systems of conservation laws in several space variables. New York: Springer-Verlag, 1984Google Scholar
- 15.Öttinger, H.C.: Stochastic processes in polymeric liquids. Berlin-Heidelberg-New York: Springer-Verlag, 1996Google Scholar