MODELS OF NONLINEAR ACOUSTICS VIEWED AS AN APPROXIMATION OF THE NAVIER-STOKES AND EULER COMPRESSIBLE ISENTROPIC SYSTEMS

Modèles d'acoustique non linéaires vus comme une approximation des sytèmes d'Euler et de Navier-Stokes compressibles et isentropiques

Adrien Dekkers (1) , Anna Rozanova-Pierrat (1)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

The derivation of different models of non linear acoustic in thermo-ellastic media as the Kuznetsov equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation and the Nonlinear Progressive wave Equation (NPE) from an isentropic Navier-Stokes/Euler system is systematized using the Hilbert type expansion in the corresponding perturbative and (for the KZK and NPE equations) paraxial ansatz. The use of small, to compare to the constant state perturbations, correctors allows to obtain the approximation results for the solutions of these models and to estimate the time during which they keep closed in the L2 norm. In the aim to compare the solutions of the exact and approximated systems in found approximation domains a global well-posedness result for the Navier-Stokes system in a half-space with time periodic initial and boundary data was obtained.

Mots clés: Non-linear acoustic; approximations of the Navier-Stokes system; Kuznetsov; KZK and NPE equations

Domaines: Equations aux dérivées partielles [math.AP]

Adrien Dekkers, Anna Rozanova-Pierrat. MODELS OF NONLINEAR ACOUSTICS VIEWED AS AN APPROXIMATION OF THE NAVIER-STOKES AND EULER COMPRESSIBLE ISENTROPIC SYSTEMS. 2019. ⟨hal-01935515v2⟩