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Mathematics > Analysis of PDEs

arXiv:2205.04632 (math)
[Submitted on 10 May 2022]

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

Authors: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.
Subjects: Analysis of PDEs (math.AP)
Cite as: arXiv:2205.04632 [math.AP]
  (or arXiv:2205.04632v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2205.04632
Related DOI: https://doi.org/10.1007/s00245-023-10003-7

Submission history

From: Wenhui Chen [view email]
[v1] Tue, 10 May 2022 02:28:44 UTC (21 KB)
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