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.
KeywordsDifferential Equation Stochastic Model Simulation Method Stochastic Differential Equation Stochastic Simulation
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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