  We study the non-autonomous weakly damped wave equation with subquintic
growth condition on the nonlinearity. Our main focus is the class of
Shatah--Struwe solutions, which satisfy the Strichartz estimates and are
coincide with the class of solutions obtained by the Galerkin method. For this
class we show the existence and smoothness of pullback, uniform, and cocycle
attractors and the relations between them. We also prove that these
non-autonomous attractors converge upper-semicontinuously to the global
attractor for the limit autonomous problem if the time-dependent nonlinearity
tends to time independent function in an appropriate way.
