Low Mach number flows in time-dependent domains

We perform a multiple time scale, single space scale analysis of a compressible fluid in a time-dependent domain, when the time variations of the boundary are small with respect to the acoustic velocity. We introduce an average operator with respect to the fast time. The averaged leading order variables satisfy modified incompressible equations, which are coupled to linear acoustic equations with respect to the fast time. We discuss possible initial-boundary data for the asymptotic equations inherited from the initial-boundary data for the compressible equations.