Global existence of weak solutions to the FENE dumbbell model of polymeric flows

• 成果类型: Article
• 署名作者: Masmoudi, Nader
• 署名单位: New York University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0399-y
• 发表日期: 2013
• 页码: 427-500
• 关键词: nonlinear fokker-planck; Navier-Stokes equations; long-time asymptotics; micro-macro model; kinetic-models; well-posedness; cauchy-problem; boltzmann equations; dilute polymers; fluid models

摘要

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.