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June  2010, 3(2): 311-324. doi: 10.3934/dcdss.2010.3.311

On the local strong solutions for the FENE dumbbell model

Ondřej Kreml 1, and  Milan Pokorný 1,

1. 

Mathematical Institute of Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic, Czech Republic

Received  March 2009 Revised  June 2009 Published  April 2010

We consider a model for the polymeric fluid which has recently been studied in [12]. We show the local-in-time existence of a strong solution to the corresponding system of partial differential equations under less regularity assumptions on the initial data than in the mentioned paper. The main difference in our approach is the use of the $L^p$ theory for the Stokes system.
Keywords: Viscoelastic fluid, $L^p$ theory., polymeric fluid, Oldroyd model, local strong solution.
Mathematics Subject Classification: Primary: 35Q35, 76D03; Secondary: 35Q3.
Citation: Ondřej Kreml, Milan Pokorný. On the local strong solutions for the FENE dumbbell model. Discrete & Continuous Dynamical Systems - S, 2010, 3 (2) : 311-324. doi: 10.3934/dcdss.2010.3.311
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