Journal
INVENTIONES MATHEMATICAE
Volume 191, Issue 2, Pages 427-500Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-012-0399-y
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Funding
- NSF-DMS grant [0703145]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1211806, 0703145] Funding Source: National Science Foundation
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Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the most classical models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows. The main difficulty is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure. In addition, this quantity controls a rescaled defect measure of the gradient of the velocity.
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