  We argue, using the AdS/CFT correspondence, that the transient dynamics of
the shear stress tensor in a strongly coupled $\mathcal{N}=4$ SYM plasma is not
described by relaxation-type, fluid dynamical equations: at long times the
equations of motion should contain a \textit{second-order} comoving derivative
of the shear stress tensor. This occurs because in this strongly-coupled system
the lowest "non-hydrodynamical" quasinormal modes associated with shear stress
possess a nonzero real part at zero wavenumber. We use Weyl invariance to
obtain the most general equations of motion containing 2 comoving derivatives
of the shear stress tensor in the transient regime that are compatible with the
symmetries. We show that the asymptotic solution of this theory valid at times
much larger than the timescale associated with the "non-hydrodynamical" modes
reproduces the well-known results previously obtained directly from the AdS/CFT
correspondence. If the QGP formed in heavy ion collisions can be at least
qualitatively understood in terms of strongly-coupled $\mathcal{N}=4$ SYM
theory, the second time derivative present in the equations of motion of the
fluid may lead to an unexpected dependence on the initial conditions for the
shear stress tensor needed in numerical hydrodynamic simulations.
