The ellipticity principle for selfsimilar polytropic potential flow
摘要
We consider self-similar potential flow for compressible gas with polytropic pressure law. Self-similar solutions arise as large-time asymptotes of general solutions, and as exact solutions of many important special cases like Mach reflection, multidimensional Riemann problems, or flow around corners. Self-similar potential flow is a quasilinear second-order PDE of mixed type which is hyperbolic at infinity (if the velocity is globally bounded). The type in each point is determined by the local pseudo-Mach number L, with L<1 resp. L>1 corresponding to elliptic resp. hyperbolic regions. We prove an ellipticity principle: the interior of a parabolic-elliptic region of a sufficiently smooth solution must be elliptic; in fact must be bounded above away from 1 by a domain-dependent function. In particular there are no open parabolic regions. We also discuss the case of slip boundary conditions at straight solid walls.
引用
@article{arxiv.math/0509332,
title = {The ellipticity principle for selfsimilar polytropic potential flow},
author = {Volker Elling and Tai-Ping Liu},
journal= {arXiv preprint arXiv:math/0509332},
year = {2007}
}