Existence of transonic solutions in the stellar wind problem with viscosity and heat conduction

Adam Bauer, Paul Carter

Research output: Contribution to journalArticlepeer-review

Abstract

The one-uid stellar wind problem for steady, radial outow is considered, including effects of heat conduction and viscosity. The associated nondimensionalized equations of conservation of mass, momentum, and energy are singularly perturbed in the large Reynolds number limit, and stellar wind profiles are constructed rigorously in this regime using geometric singular perturbation techniques. Transonic solutions, which accelerate from subsonic to supersonic speeds, are identified as folded saddle canard trajectories lying in the intersection of a subsonic saddle slow manifold and a supersonic repelling slow manifold, returning to subsonic speeds through a viscous layer shock, the location of which is determined by the associated far-field boundary conditions.

Original languageEnglish (US)
Pages (from-to)262-298
Number of pages37
JournalSIAM Journal on Applied Dynamical Systems
Volume20
Issue number1
DOIs
StatePublished - Feb 18 2021

Bibliographical note

Funding Information:
∗Received by the editors January 21, 2020; accepted for publication (in revised form) by M. Beck November 23, 2020; published electronically February 18, 2021. https://doi.org/10.1137/20M1314240 Funding: This work was supported by NSF grant DMS-1815315. †Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL 61820 USA (adammb4@illinois.edu). ‡School of Mathematics, University of Minnesota, Twin Cities, MN 55455 USA (pcarter@umn.edu).

Publisher Copyright:
© 2021 Society for Industrial and Applied Mathematics Publications. All rights reserved.

Keywords

  • Canards
  • Geometric singular perturbation theory
  • Stellar wind

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