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The derivation of different models of non linear acoustic in thermo-ellasticmedia as the Kuznetsov equation, the Khokhlov-Zabolotskaya-Kuznetsov (KZK)equation and the Nonlinear Progressive wave Equation (NPE) from an isentropicNavier-Stokes/Euler system is systematized using the Hilbert type expansion inthe corresponding perturbative and (for the KZK and NPE equations) paraxialansatz . The use of small, to compare to the constant state perturbations,correctors allows to obtain the approximation results for the solutions ofthese models and to estimate the time during which they keep closed in the L2norm. The KZK and NPE equations are also considered as paraxial approximationsof the Kuznetsov equation, which is a model obtained only by perturbations fromthe Navier-Stokes/Euler system. The Westervelt equation is obtained as anonlinear approximation of the Kuznetsov equation. In the aim to compare thesolutions of the exact and approximated systems in found approximation domainsthe well-posedness results (for the Navier-Stokes system and the Kuznetsovequation in a half-space with periodic in time initial and boundary data) wereobtained.

Models of nonlinear acoustics viewed as an approximation of the Navier-Stokes and Euler compressible isentropicsystems