Well-posedness and exponential decay of solutions for the Blackstock-Crighton-Kuznetsov equation

Abstract

The present work provides well-posedness and exponential decay results for the Blackstock-Crighton-Kuznetsov equation arising in the modeling of nonlinear acoustic wave propagation in thermally relaxing viscous fluids. First, we treat the associated linear equation by means of operator semigroups. Moreover, we derive energy estimates which we will use in a fixed-point argument in order to obtain well-posedness of the Blackstock-Crighton-Kuznetsov equation. Using a classical barrier argument we prove exponential decay of solutions.

18 pages

References in corpus (2)

• Well-Posedness and asymptotic behavior of solutions for the Blackstock-Crighton-Westervelt equation
• Relaxation of regularity for the Westervelt equation by nonlinear damping with application in acoustic-acoustic and elastic-acoustic coupling

Cited by in corpus (4)

• Nonlinear Acoustics and Shock Formation in Lossless Barotropic Green--Naghdi Fluids
• Asymptotic behaviors for Blackstock's model of thermoviscous flow
• Optimal regularity and exponential stability for the Blackstock-Crighton equation in $L_p$-spaces with Dirichlet and Neumann boundary conditions
• Large-time asymptotic behaviors for linear Blackstock's model of thermoviscous flow