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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...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Hindawi Publishing Corporation
2014
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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 |
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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 |
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