In this paper, we mainly study global existence and optimal L2 decay rate
of weak solutions to the co-rotation Hooke dumbbell model. This micro-macro
model is a coupling of the Navier-Stokes equation with a nonlinear
Fokker-Planck equation. Based on the defect measure propagation method, we
prove that the co-rotation Hooke dumbbell model admits a global weak solution
provided the initial data under different integrability conditions. Moreover,
we obtain optimal long time decay rate in L2 for the weak solutions obtained
by the Fourier splitting method