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arXiv · 2205.04632

Large-time asymptotic behaviors for linear Blackstock's model of thermoviscous flow

Wenhui Chen·Hiroshi Takeda
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Abstract

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

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Wenhui Chen, Hiroshi Takeda. 2022-05-10. Large-time asymptotic behaviors for linear Blackstock's model of thermoviscous flow. https://doi.org/10.1007/s00245-023-10003-7

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