Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles

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

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Author(s)

  • Gui-Qiang G. Chen
  • Fei-Min Huang
  • Tian-Yi Wang
  • Wei Xiang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)946-1008
Number of pages63
Journal / PublicationAdvances in Mathematics
Volume346
Online published19 Feb 2019
Publication statusPublished - 13 Apr 2019

Abstract

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic–sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.

Research Area(s)

  • Steady Euler flows, Large vorticity, Characteristic discontinuities, Free boundary, Existence, Uniqueness

Citation Format(s)

Steady Euler flows with large vorticity and characteristic discontinuities in arbitrary infinitely long nozzles. / Chen, Gui-Qiang G.; Huang, Fei-Min; Wang, Tian-Yi et al.

In: Advances in Mathematics, Vol. 346, 13.04.2019, p. 946-1008.

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