On the New Multiscale Rodlike Model of Polymeric Fluids

This paper is concerned with the well-posedness for the new rigid rodlike model in a polymeric fluid recently proposed by W.N. E and P.W. Zhang [Meth. Appl. Anal., 13 (2006), pp. 181–198]. The constitutive relations considered in this work are motivated by the kinetic theory. The micro equations involve five independent spatial variables (degrees of freedom): two in the configuration domain and three in the macro flow domain. We obtain the local existence of solutions with large initial data and also global existence of solutions with small Deborah and Reynolds constants in periodic domains.