Global existence and estimates for Blackstock's model of thermoviscous flow with second sound phenomena

According to the Lighthill scheme of approximation procedures, we establish the Blackstock-Cattaneo model in this paper to describe nonlinear acoustics' propagations with second sound phenomena in per-fect gases under the irrotational flow, which is an approximated higher-order equation for Navier-Stokes-Cattaneo equations. This paper is devoted to the mathematical analysis of the linear and nonlinear higher-order evolution equations in Rn. Concerning the linearized Cauchy problem for the Blackstock-Cattaneo equation, by means of the Fourier analysis and the WKB analysis, we will derive sharp L2 estimates of solutions with additional L1 regularity for initial data. For another, we demonstrate global (in time) well-posedness for the nonlinear Blackstock-Cattaneo equation with small initial data and suitable regularity of Sobolev solutions.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

The paper introduces the Blackstock-Cattaneo model based on the Lighthill scheme to describe nonlinear acoustics' propagations with second sound phenomena. It focuses on the mathematical analysis of linear and nonlinear higher-order evolution equations in Rn and investigates the linearized Cauchy problem and global well-posedness of the nonlinear Blackstock-Cattaneo equation.