Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations

Details Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations Global Steady Subsonic Flows through Infinitely Long Nozzles for the Full Euler Equations

2011-12-31

arxiv.org/abs/1201.0291v2

Mathematics

Analysis of PDEs

32 pages, 1 figure. arXiv admin note: text overlap with arXiv:0907.3276 by other authors

Scientific paper

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 from 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, have been clarified.

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