Blowup for C² solutions of the N-dimensional Euler–Poisson equations in Newtonian cosmology

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Pressureless Euler–Poisson equations with attractive forces are standard models in Newtonian cosmology. In this article, we further develop the spectral dynamics method and apply a novel spectral-dynamics-integration method to study the blowup conditions for C² solutions with a bounded domain, ‖X(t)‖⩽X₀, where ‖⋅‖ denotes the volume and X₀ is a positive constant. In particular, we show that if the cosmological constant Λ<M/X₀, with the total mass M, then the non-trivial C² solutions in Rᴺ with the initial condition the Ω₀ᵢj(x)=½[∂ᵢuʲ(0,x)−∂juⁱ(0,x)]=0 blow up at a finite time.  Copyright © 2014 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)972-978
JournalJournal of Mathematical Analysis and Applications
Volume415
Issue number2
Early online dateFeb 2014
DOIs
Publication statusPublished - Jul 2014

Fingerprint

Cosmology
Euler-Poisson Equations
Blow-up
Cosmological Constant
Standard Model
Bounded Domain
Initial conditions
Denote

Citation

Yuen, M. (2014). Blowup for C² solutions of the N-dimensional Euler–Poisson equations in Newtonian cosmology. Journal of Mathematical Analysis and Applications, 415(2), 972-978.

Keywords

  • Newtonian cosmology
  • Euler–Poisson equations
  • Initial value problem
  • Blowup
  • Spectral-dynamics-integration method
  • Attractive forces
  • C² solutions
  • Bounded domain
  • Rᴺ