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arXiv · 1112.1750

Local Uniqueness of Steady Spherical Transonic Shock-fronts for the Three-Dimensional Full Euler Equations

Gui-Qiang G. Chen·Hairong Yuan
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Abstract

We establish the local uniqueness of steady transonic shock solutions with spherical symmetry for the three-dimensional full Euler equations. These transonic shock-fronts are important for understanding transonic shock phenomena in divergent nozzles. From mathematical point of view, we show the uniqueness of solutions of a free boundary problem for a multidimensional quasilinear system of mixed-composite elliptic--hyperbolic type. To this end, we develop a decomposition of the Euler system which works in a general Riemannian manifold, a method to study a Venttsel problem of nonclassical nonlocal elliptic operators, and an iteration mapping which possesses locally a unique fixed point. The approach reveals an intrinsic structure of the steady Euler system and subtle interactions of its elliptic and hyperbolic part.

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Gui-Qiang G. Chen, Hairong Yuan. 2011-12-08. Local Uniqueness of Steady Spherical Transonic Shock-fronts for the Three-Dimensional Full Euler Equations. https://arxiv.org/abs/1112.1750

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