Low Mach Number Limit of Viscous Polytropic Flows: Formal Asymptotics in the Periodic Case

Abstract

This article is devoted to the low Mach number limit of weak solutions to the compressible Navier–Stokes equations for polytropic fluids with periodic boundary conditions and ill‐prepared data. We derive formally the equation satisfied by the mean value of the velocity and the equations governing the dynamics of the nonlinear acoustic waves in dimension d = 2 or 3.