Approximation of a compressible Navier-Stokes system by non-linear acoustical models

We analyse the existing derivation of the models of non-linear acoustics such as the Kuznetsov equation, the NPE equation and the KZK equation. The technique of introducing a corrector in the derivation ansatz allows us to consider the solutions of these equations as approximations of the solution of the initial system (a compressible Navier-Stokes/Euler system). The validation of the approximation ansatz is given for the KZK equation case.