Models of nonlinear acoustics viewed as an approximation of the Navier–Stokes and Euler compressible isentropic systems

The Cauchy–Dirichlet problem for the Moore–Gibson–Thompson equation

“…(iii) While a trace regularity result for the second-order normal derivative cannot be obtained, we wonder whether g ∈ H 2 (Σ) implies ∂w/∂ν ∈ H 1 (Σ). (iv) Instrumental to the study of an inverse problem, the regularity of boundary trace (12) is shown in [32] for the special case of homogeneous boundary data. The said result is contained in our Proposition 6 which pertains to the general non-homogeneous case, and a fortiori in Theorem 1 (a).…”

“…(formulated in terms of the acoustic velocity potential ψ); all constants that occurr in the equations are positive: c, b are the speed and diffusivity of sound, ρ > 0 is the mass density, β a > 1. The connections of the Westervelt and Kuznetsov (and Khokhlov-Zabolotskaya-Kuznetsov) models with the Navier-Stokes and Euler compressible system is explored in the recent [12]. A well-recognized issue which arises in the modeling of propagation of acoustic and thermal waves is the paradox of heat conduction, namely, the incongruity between the infinite speed of propagation of a thermal disturbance with the principle of classical mechanics known as causality; see, e.g., [21] and its references.…”