Two timescales asymptotes of the weakly compressible Stokes system (Q1678249)

This paper is concerned with the study of an asymptotic study of the weakly compressible Stokes (WCS) system, which is a linearization of the compressible Navier-Stokes-Fourier system about the homogeneous state. Using the standard Arzelà-Ascoli Theorem, a proof of the strong convergence to the acoustic system in the periodic domain is given; the filtering method is applied to prove the incompressible Stokes limit in periodic domain. The paper ends with the construction of a viscous-thermal boundary layer and to give a strong convergence of the Stokes limit with Dirichlet boundary condition.