Large-Time Asymptotic Behaviors for Linear Blackstock’s Model of Thermoviscous Flow

In the classical theory of acoustic waves, Blackstock's model was proposed in 1963 to characterize propagation sound thermoviscous fluids. this paper, we investigate large-time asymptotic behaviors linear Cauchy problem for general (that is, without Becker's assumption on monatomic perfect gases). We derive first- and second-order profiles solution as $t\gg1$ by applying refined WKB analysis Fourier analysis. Our results not only improve optimal estimates [Chen-Ikehata-Palmieri, \emph{Indiana Univ. Math. J.} (2023)] lower dimensional cases, but also illustrate leading term novel with additional weighted $L^1$ data.