On a micro-macro model for polymeric fluids near equilibrium

In this paper, we study a micro-macro model for polymeric fluid. The system involves coupling between the macroscopic momentum equation and a micro-scopic evolution equation describing the combined effects of the microscopic potential and thermofluctuation. We employ an energetic variation procedure to explore the relation between the macroscopic transport of the particles and the induced elastic stress due to the microscopic structure. For the initial data not far from the equilibrium, we prove the global existence and uniqueness of classical solutions to the system.