Emergence of peaked singularities in the Euler-Poisson system
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909313384054784 |
|---|---|
| author | Bae, Junsik Moon, Sang-Hyuck Woo, Kwan |
| author_facet | Bae, Junsik Moon, Sang-Hyuck Woo, Kwan |
| contents | We consider the one-dimensional Euler-Poisson system equipped with the Boltzmann relation and provide the exact asymptotic behavior of the peaked solitary wave solutions near the peak. This enables us to study the cold ion limit of the peaked solitary waves with the sharp range of Hölder exponents. Furthermore, we provide numerical evidence for $C^1$ blow-up solutions to the pressureless Euler-Poisson system, whose blow-up profiles are asymptotically similar to its peaked solitary waves and exhibit a different form of blow-up compared to the Burgers-type (shock-like) blow-up. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08018 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Emergence of peaked singularities in the Euler-Poisson system Bae, Junsik Moon, Sang-Hyuck Woo, Kwan Analysis of PDEs We consider the one-dimensional Euler-Poisson system equipped with the Boltzmann relation and provide the exact asymptotic behavior of the peaked solitary wave solutions near the peak. This enables us to study the cold ion limit of the peaked solitary waves with the sharp range of Hölder exponents. Furthermore, we provide numerical evidence for $C^1$ blow-up solutions to the pressureless Euler-Poisson system, whose blow-up profiles are asymptotically similar to its peaked solitary waves and exhibit a different form of blow-up compared to the Burgers-type (shock-like) blow-up. |
| title | Emergence of peaked singularities in the Euler-Poisson system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.08018 |