  We study a fundamental model in nonlinear acoustics, precisely, the general
Blackstock's model (that is, without Becker's assumption) in the whole space
$\mathbb{R}^n$. This model describes nonlinear acoustics in perfect gases under
the irrotational flow. By means of the Fourier analysis we will derive $L^2$
estimates for the solution of the linear homogeneous problem and its
derivatives. Then, we will apply these estimates to study three different
topics: the optimality of the decay estimates in the case $n\geqslant 5$ and
the optimal growth rate for the $L^2$-norm of the solution for $n=3,4$; the
singular limit problem in determining the first- and second-order profiles for
the solution of the linear Blackstock's model with respect to the small thermal
diffusivity; the proof of the existence of global (in time) small data Sobolev
solutions with suitable regularity for a nonlinear Blackstock's model.
