Global steady subsonic flows through infinitely long nozzles for the full Euler equations

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)2888-2919
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume44
Issue number4
Publication statusPublished - 2012
Externally publishedYes

Abstract

We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of second order in terms of the stream function. It is established that, when the oscillation of the entropy and Bernoulli functions at the upstream is sufficiently small in C 1,1 and the mass flux is in a suitable regime, there exists a unique global subsonic solution in a suitable class of general nozzles. The assumptions are required to prevent the occurrence of supersonic bubbles inside the nozzles. The asymptotic behavior of subsonic flows at the downstream and upstream, as well as the critical mass flux, has been clarified. © 2012 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Asymptotic behavior, Bernoulli function, Critical mass flux, Entropy function, Existence, Full Euler equations, Global subsonic flows, Infinitely long nozzles, Reduction, Second-order nonlinear equations, Steady flows, Stream function, Supersonic bubbles