  We use radial estimates for pseudodifferential operators to describe long
time evolution of solutions to $ i u_t - P u = f $ where $ P $ is a
self-adjoint 0th order pseudodifferential operator satisfying hyperbolic
dynamical assumptions and where $ f $ is smooth. This is motivated by recent
results of Colin de Verdi\`ere and Saint-Raymond [arXiv:1801.05582] concerning
a microlocal model of internal waves in stratified fluids.
