Global existence and mean-field limit for a stochastic interacting particle system of signed Coulomb charges
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909357543784448 |
|---|---|
| author | van Meurs, Patrick Peletier, Mark A. Slangen, Thomas |
| author_facet | van Meurs, Patrick Peletier, Mark A. Slangen, Thomas |
| contents | We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles that either all repel each other or all attract each other, this system contains both `positive' and `negative' particles. Equal signs repel and opposite signs attract each other; apart from the sign, the potential is the same.
We derive results on well-posedness of the system, on the type of collisions that can occur, and on the mean-field limit as the number of particles tends to infinity. Our results demonstrate that the signed system shares features of both the fully repulsive and the fully attractive cases. Our proof method is inspired by the work of Fournier and Jourdain (The Annals of Applied Probability, 27, pp. 2807-2861, 2017) on the fully attractive case; we construct an approximate system of equations, establish uniform estimates, and use tightness to pass to limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and mean-field limit for a stochastic interacting particle system of signed Coulomb charges van Meurs, Patrick Peletier, Mark A. Slangen, Thomas Probability Mathematical Physics Analysis of PDEs 65C35, 35K55, 60H10 We study a system of stochastic differential equations with singular drift which describes the dynamics of signed particles in two dimensions interacting by the Coulomb potential. In contrast to the well-studied cases of identical particles that either all repel each other or all attract each other, this system contains both `positive' and `negative' particles. Equal signs repel and opposite signs attract each other; apart from the sign, the potential is the same. We derive results on well-posedness of the system, on the type of collisions that can occur, and on the mean-field limit as the number of particles tends to infinity. Our results demonstrate that the signed system shares features of both the fully repulsive and the fully attractive cases. Our proof method is inspired by the work of Fournier and Jourdain (The Annals of Applied Probability, 27, pp. 2807-2861, 2017) on the fully attractive case; we construct an approximate system of equations, establish uniform estimates, and use tightness to pass to limits. |
| title | Global existence and mean-field limit for a stochastic interacting particle system of signed Coulomb charges |
| topic | Probability Mathematical Physics Analysis of PDEs 65C35, 35K55, 60H10 |
| url | https://arxiv.org/abs/2410.15855 |