We consider the Cauchy problem for incompressible viscoelastic fluids in the
whole space Rd (d=2,3). By introducing a new decomposition via
Helmholtz's projections, we first provide an alternative proof on the existence
of global smooth solutions near equilibrium. Then under additional assumptions
that the initial data belong to L1 and their Fourier modes do not degenerate
at low frequencies, we obtain the optimal L2 decay rates for the global
smooth solutions and their spatial derivatives. At last, we establish the
weak-strong uniqueness property in the class of finite energy weak solutions
for the incompressible viscoelastic system.Comment: 28 pages, finished in 2012, accepted by DCDS-A in 201