Multiple scattering of acoustic waves by small sound-soft obstacles in two dimensions: Mathematical justification of the Foldy–Lax model

We are concerned with a two-dimensional problem which models the scattering of a time-harmonic acoustic wave by an arbitrary number of sound-soft circular obstacles. Assuming that their radii are small compared to the wavelength, we propose a mathematical justification of different levels of asymptotic models available in the physical literature, including the so-called Foldy–Lax model. ► Different levels of asymptotic models are introduced. ► Three points of view are adopted: physical, asymptotic and mathematical. ► Error estimates for each model are provided.