The ellipticity principle for selfsimilar polytropic potential flow
| dc.creator | Elling, Volker | |
| dc.creator | Liu, Tai-Ping | |
| dc.date | 2005-09-14 | |
| dc.date.accessioned | 2026-07-07T05:23:13Z | |
| dc.date.available | 2026-07-07T05:23:13Z | |
| dc.description | 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 $L$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0509332 | |
| dc.identifier | http://arxiv.org/abs/math/0509332 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76348 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.title | The ellipticity principle for selfsimilar polytropic potential flow | |
| dc.type | text |