Analytical blowup solutions to the 2-dimensional isothermal Euler–Poisson equations of gaseous stars

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Abstract

We study the Euler–Poisson equations of describing the evolution of the gaseous star in astrophysics. Firstly, we construct a family of analytical blowup solutions for the isothermal case in R². Furthermore the blowup rate of the above solutions is also studied and some remarks about the applicability of such solutions to the Navier–Stokes–Poisson equations and the drift-diffusion model in semiconductors are included. Finally, for the isothermal case (y = 1), the result of Makino and Perthame for the tame solutions is extended to show that the life span of such solutions must be finite if the initial data is with compact support. Copyright © 2007 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)445-456
JournalJournal of Mathematical Analysis and Applications
Volume341
Issue number1
DOIs
Publication statusPublished - May 2008

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Euler-Poisson Equations
Drift-diffusion Model
Blow-up Rate
Blow-up Solution
Astrophysics
Life Span
Compact Support
Stars
Semiconductors
Star
Family
Semiconductor materials

Citation

Yuen, M. (2008). Analytical blowup solutions to the 2-dimensional isothermal Euler–Poisson equations of gaseous stars. Journal of Mathematical Analysis and Applications, 341(1), 445-456. doi: 10.1016/j.jmaa.2007.10.026

Keywords

  • Blowup solutions
  • Euler–Poisson equations
  • 2-Dimensional
  • Isothermal
  • Blowup rates