  High frequencies at which ultrasonic waves travel give rise to nonlinear
phenomena. In thermoviscous fluids, these are captured by Blackstock's acoustic
wave equation with strong damping. We revisit in this work its well-posedness
analysis. By exploiting the parabolic-like character of this equation due to
strong dissipation, we construct a time-weighted energy framework for
investigating its local solvability. In this manner, we obtain the small-data
well-posedness on bounded domains under less restrictive regularity assumptions
on the initial conditions compared to the known results. Furthermore, we prove
that such initial boundary-value problems for the Blackstock equation are
globally solvable and that their solution decays exponentially fast to the
steady state.
