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 $d\ge 2,\,d\ne 4$, 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 appe...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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American Mathematical Society
2022
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| _version_ | 1797110034039046144 |
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| author | Carrillo de la Plata, JA Shu, R |
| author_facet | Carrillo de la Plata, JA Shu, R |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | We consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension $d\ge 2,\,d\ne 4$, 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 global smooth solution requires the period of every characteristic to be identical. |
| first_indexed | 2024-03-07T07:49:35Z |
| format | Journal article |
| id | oxford-uuid:26b1e0df-b99d-425c-bfd6-e28df16754ea |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:49:35Z |
| publishDate | 2022 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:26b1e0df-b99d-425c-bfd6-e28df16754ea2023-07-04T13:25:54ZExistence of radial global smooth solutions to the pressureless Euler-Poisson equations with quadratic confinementJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:26b1e0df-b99d-425c-bfd6-e28df16754eaEnglishSymplectic ElementsAmerican Mathematical Society2022Carrillo de la Plata, JAShu, RWe consider the pressureless Euler-Poisson equations with quadratic confinement. For spatial dimension $d\ge 2,\,d\ne 4$, 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 global smooth solution requires the period of every characteristic to be identical. |
| spellingShingle | Carrillo de la Plata, JA Shu, R 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 |
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