Linearization method and sharp thresholds for spherically symmetric multidimensional pressureless Euler-Poisson equations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866929689045499904 |
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| author | Rozanova, Olga S. Turzynsky, Marko K. |
| author_facet | Rozanova, Olga S. Turzynsky, Marko K. |
| contents | We show that the question about the criterion of a singularity formation for radially symmetric solutions to the Cauchy problem for a fairly wide class of equations related to the pressureless Euler-Poisson equations can be reduced to the study of solutions to a linear homogeneous ordinary differential equation. In some cases, such a criterion can be obtained in terms of the initial data. In the remaining cases, it is possible to construct a simple numerical procedure, on the basis of which the question about preserving smoothness for any set of initial data can be solved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Linearization method and sharp thresholds for spherically symmetric multidimensional pressureless Euler-Poisson equations Rozanova, Olga S. Turzynsky, Marko K. Analysis of PDEs Mathematical Physics 35L60 35L67 35Q60 35Q85 We show that the question about the criterion of a singularity formation for radially symmetric solutions to the Cauchy problem for a fairly wide class of equations related to the pressureless Euler-Poisson equations can be reduced to the study of solutions to a linear homogeneous ordinary differential equation. In some cases, such a criterion can be obtained in terms of the initial data. In the remaining cases, it is possible to construct a simple numerical procedure, on the basis of which the question about preserving smoothness for any set of initial data can be solved. |
| title | Linearization method and sharp thresholds for spherically symmetric multidimensional pressureless Euler-Poisson equations |
| topic | Analysis of PDEs Mathematical Physics 35L60 35L67 35Q60 35Q85 |
| url | https://arxiv.org/abs/2501.16455 |