  In this paper, we consider the 3D Jordan--Moore--Gibson--Thompson equation
arising in nonlinear acoustics. First, we prove that the solution exists
globally in time provided that the lower order Sobolev norms of the initial
data are considered to be small, while the higher-order norms can be
arbitrarily large. This improves some available results in the literature.
Second, we prove a new decay estimate for the linearized model and removing the
$L^1$-assumption on the initial data. The proof of this decay estimate is based
on the high-frequency and low-frequency decomposition of the solution together
with an interpolation inequality related to Sobolev spaces with negative order.
