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We prove that the divergence-free component of the compressible Eulerequations with solid-wall boundary condition converges strongly towards theincompressible Euler equations at the same order as the Mach number. Generalinitial data are considered and are not necessarily close to thedivergence-free state. Thus, large amplitude of fast oscillations persist andinteract through nonlinear coupling without any dissipative or dispersivemechanism. It is then shown, however, that the contribution from fastoscillations to the slow dynamics through nonlinear coupling is of the sameorder as the Mach number when averaged in time. The structural condition of avorticity equation plays a key role in our argument.

Low-Mach-number Euler equations with solid-wall boundary condition and general initial data