Global existence of weak solutions to macroscopic models of polymeric flows
The finite extensible nonlinear elastic (FENE) model, introduced by Peterlin describing a complex mixture of polymer and liquid is considered. The main result of this paper concerns the proof of the global existence of weak solutions of this model. An important problem is pointed out: the obtained results can be extended to the Oldroyd-B model, corresponding to the Hoken spring model at the microscopic level, when the extra stress tensor \(\tau\) belongs to \(L^2\). Even if in general this condition is not verified, the author proves in the last part a global existence theorem for a modified Oldroyd-B model that yields an \(L^2\) bound of \(\tau\). The main mathematical tool is the approximation of the initial system by a sequence of more regular problems (for which the existence is easily proved) and the use of a weak compactness argument. This point is rigorously analysed in section 3, also related to the Chacon limit (briefly recalled in the Appendix).
scientific article; zbMATH DE number 5986957
scientific article