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Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement
We consider the pressureless Euler–Poisson equations with quadratic confinement. For spatial dimension [Formula: see text] , we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulated explicitly in terms of the initial data. This condition a...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Springer Berlin Heidelberg
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10393895/ https://www.ncbi.nlm.nih.gov/pubmed/37538138 http://dx.doi.org/10.1007/s00205-023-01905-5 |
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author | Carrillo, José A. Shu, Ruiwen |
author_facet | Carrillo, José A. Shu, Ruiwen |
author_sort | Carrillo, José A. |
collection | PubMed |
description | We consider the pressureless Euler–Poisson equations with quadratic confinement. For spatial dimension [Formula: see text] , we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulated explicitly in terms of the initial data. This condition appears to be much more restrictive than the critical-threshold conditions commonly seen in the study of Euler-type equations. To obtain our results, the key observation is that every characteristic satisfies a periodic ODE system, and the existence of a global smooth solution requires the period of every characteristic to be identical. |
format | Online Article Text |
id | pubmed-10393895 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer Berlin Heidelberg |
record_format | MEDLINE/PubMed |
spelling | pubmed-103938952023-08-03 Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement Carrillo, José A. Shu, Ruiwen Arch Ration Mech Anal Original Article We consider the pressureless Euler–Poisson equations with quadratic confinement. For spatial dimension [Formula: see text] , we give a necessary and sufficient condition for the existence of radial global smooth solutions, which is formulated explicitly in terms of the initial data. This condition appears to be much more restrictive than the critical-threshold conditions commonly seen in the study of Euler-type equations. To obtain our results, the key observation is that every characteristic satisfies a periodic ODE system, and the existence of a global smooth solution requires the period of every characteristic to be identical. Springer Berlin Heidelberg 2023-08-01 2023 /pmc/articles/PMC10393895/ /pubmed/37538138 http://dx.doi.org/10.1007/s00205-023-01905-5 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . |
spellingShingle | Original Article Carrillo, José A. Shu, Ruiwen Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title | Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title_full | Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title_fullStr | Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title_full_unstemmed | Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title_short | Existence of Radial Global Smooth Solutions to the Pressureless Euler–Poisson Equations with Quadratic Confinement |
title_sort | existence of radial global smooth solutions to the pressureless euler–poisson equations with quadratic confinement |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10393895/ https://www.ncbi.nlm.nih.gov/pubmed/37538138 http://dx.doi.org/10.1007/s00205-023-01905-5 |
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