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

The derivation of different models of non linear acoustic in thermo-elastic media as the Kuznetsov equation, the Khokhlov-Zabolotslcaya-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 correctors, to compare to the constant state perturbations, allows to obtain the approximation results for the solutions of these models and to estimate the time during which they keep closed in the L-2 norm. In the aim to compare the solutions of the exact and approximate 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.