  Muon-spin-relaxation measurements have been performed for the partially
Zn-substituted La_2-x_Sr_x_Cu_1-y_Zn_y_O_4_ with y=0-0.10 in the overdoped
regime up to x=0.30. In the 3 % Zn-substituted samples up to x=0.27,
exponential-like depolarization of muon spins has been observed at low
temperatures, indicating Zn-induced slowing-down of the Cu-spin fluctuations.
The depolarization rate decreases with increasing x and almost no fast
depolarization of muon spins has been observed for x=0.30 where
superconductivity disappears. The present results suggest that the dynamical
stripe correlations exist in the whole superconducting regime of
La_2-x_Sr_x_CuO_4_ and that there is no quantum critical point at x~0.19.
