Incompressible limit on thin domains with periodic boundary condition

Abstract

We consider convergence to the incompressible Navier–Stokes equations/Euler equations for compressible viscous flows on periodic thin domain with general initial data. Compared with Caggio et al (2020 Nonlinearity 33 840–863), where similar problems are considered in the whole space, we have to deal with the persistence of acoustic waves. We prove that the weak solutions in the 3D domain converge weakly/strongly to the solutions of the 2D incompressible Navier–Stokes equations/Euler equations when the Mach number ɛ goes to 0 as well as the thickness δ/the viscosity goes to 0.