Three-Dimensional Full Euler Flows with Nontrivial Swirl in Axisymmetric Nozzles

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

17 Scopus Citations
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Detail(s)

Original languageEnglish
Pages (from-to)2740-2772
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume50
Issue number3
Online published24 May 2018
Publication statusPublished - 2018

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Abstract

We are concerned with the unique existence of three-dimensional steady compressible full Euler flows through arbitrary infinitely long axisymmetric and piecewise smooth nozzles with nontrivial swirl. We develop a new approach to prove the nondegeneracy of the axial velocity based on the observation of the potential flow. A modified argument is also employed to handle the stagnation at the corner points. It is the first result on the three-dimensional compressible Euler flow with more than one nonzero and large vorticity. In order to show it, one new stream-conserved quantity is constructed. Finally, the minimum flux limits and the incompressible limits are considered. Via the incompressible limit, we also establish the unique existence of incompressible Euler flows with nontrivial swirl. The methods and techniques developed in this paper are also helpful to other related problems.

Research Area(s)

  • Axisymmetric nozzles, Full Euler equations, Nontrivial swirl, Stream function

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Citation Format(s)

Three-Dimensional Full Euler Flows with Nontrivial Swirl in Axisymmetric Nozzles. / Deng, Xuemei; Wang, Tian-Yi; Xiang, Wei.
In: SIAM Journal on Mathematical Analysis, Vol. 50, No. 3, 2018, p. 2740-2772.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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