The Zero-Mach Limit of Compressible Euler Equations

摘要

The aim of this paper is to prove that compressible Euler equations in two and three space dimensions converge to incompressible Euler equations in the limit as the Mach number tends to zero. No smallness restrictions are imposed on the initial velocity, or the time interval. We assume instead that the incompressible flows exists and is reasonably smooth on a given time interval, and prove that compressible flows converge uniformly on that time interval.