Cargando…

Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions

We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N). For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing eq...

Descripción completa

Detalles Bibliográficos
Autores principales: Wong, Sen, Yuen, Manwai
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3985311/
https://www.ncbi.nlm.nih.gov/pubmed/24982967
http://dx.doi.org/10.1155/2014/580871
_version_ 1782311555277258752
author Wong, Sen
Yuen, Manwai
author_facet Wong, Sen
Yuen, Manwai
author_sort Wong, Sen
collection PubMed
description We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N). For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P = Kρ (γ), where ρ is the density function, K is a constant, and γ > 1, we can show that the nontrivial C (1) solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include r (N−1)ln(r + 1), r (N−1) e (r), r (N−1)(r (3) − 3r (2) + 3r + ε), r (N−1)sin((π/2)(r/R)), and r (N−1)sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.
format Online
Article
Text
id pubmed-3985311
institution National Center for Biotechnology Information
language English
publishDate 2014
publisher Hindawi Publishing Corporation
record_format MEDLINE/PubMed
spelling pubmed-39853112014-06-30 Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions Wong, Sen Yuen, Manwai ScientificWorldJournal Research Article We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N). For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P = Kρ (γ), where ρ is the density function, K is a constant, and γ > 1, we can show that the nontrivial C (1) solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include r (N−1)ln(r + 1), r (N−1) e (r), r (N−1)(r (3) − 3r (2) + 3r + ε), r (N−1)sin((π/2)(r/R)), and r (N−1)sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given. Hindawi Publishing Corporation 2014 2014-03-30 /pmc/articles/PMC3985311/ /pubmed/24982967 http://dx.doi.org/10.1155/2014/580871 Text en Copyright © 2014 S. Wong and M. Yuen. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Wong, Sen
Yuen, Manwai
Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title_full Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title_fullStr Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title_full_unstemmed Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title_short Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions
title_sort blowup phenomena for the compressible euler and euler-poisson equations with initial functional conditions
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3985311/
https://www.ncbi.nlm.nih.gov/pubmed/24982967
http://dx.doi.org/10.1155/2014/580871
work_keys_str_mv AT wongsen blowupphenomenaforthecompressibleeulerandeulerpoissonequationswithinitialfunctionalconditions
AT yuenmanwai blowupphenomenaforthecompressibleeulerandeulerpoissonequationswithinitialfunctionalconditions