LOW MACH NUMBER LIMIT OF STEADY EULER FLOWS IN MULTI-DIMENSIONAL NOZZLES

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1191-1220
Journal / PublicationCommunications in Mathematical Sciences
Volume18
Issue number5
Publication statusPublished - 2020

Abstract

In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with the conservative extra force to the corresponding incompressible flow, which is free from the conservative extra force effect, as the Mach number goes to zero. The limit is on the Holder space and is unique. Moreover, the convergence rate is of order ε2, which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

Research Area(s)

  • Convergence rate, Homentropic euler equations, Low mach number limit, Multidimensional nozzles, Steady flow