Low Mach number limit of steady flows through infinite multidimensional largely-open nozzles

Abstract

In this paper, we justify of the low Mach number limit of the steady irrotational Euler flow through infinite multidimensional largely-open nozzles. Firstly, the existence and uniqueness of the incompressible flow are proved. Then, the uniform estimates on the compressibility parameter ε, which is singular for the flows, are established via a variational approach based on the compressible-incompressible difference functions. The limit is in the Hölder space and is unique. Moreover, the convergence rate is of order ε2 including the pressure. And, for the compressible case, the extra force influences the asymptotic behaver to the open end, while the effect vanishes in the limiting process from compressible flows to the incompressible ones. Also, for the compressible flows with general conservative forces, the well-posedness of subsonic solution are given, which leads to the existence of subsonic-sonic limit solutions.