论文标题
线性黑stock的热雾模型的大型渐近行为
Large-time asymptotic behaviors for linear Blackstock's model of thermoviscous flow
论文作者
论文摘要
在声波的经典理论中，在1963年提出了Blackstock的模型，以表征热雾液中声音的传播。在本文中，我们研究了BlackStock将军模型的线性库奇问题的大渐近行为（也就是说，没有贝克尔对单变性的完美气体的假设）。通过应用精制的WKB分析和傅立叶分析，我们将解决方案的一阶和二阶渐近概谱作为$ t \ gg1 $。我们的结果不仅改善了[Chen-kikhata-palmieri，\ emph {Indiana Univ。数学。 J.}（2023）]对于较低的尺寸案例，但也说明了解决方案的最佳前期和新颖的二阶轮廓，并使用了额外的加权$ l^1 $数据。
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.
