Damping versus oscillations for a gravitational Vlasov-Poisson system
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908459408031744 |
|---|---|
| author | Hadzic, Mahir Rein, Gerhard Schrecker, Matthew Straub, Christopher |
| author_facet | Hadzic, Mahir Rein, Gerhard Schrecker, Matthew Straub, Christopher |
| contents | We consider a family of isolated inhomogeneous steady states to the gravitational Vlasov-Poisson system with a point mass at the centre. They are parametrised by the polytropic index $k>1/2$, so that the phase space density of the steady state is $C^1$ at the vacuum boundary if and only if $k>1$. We prove the following sharp dichotomy result: if $k>1$ the linear perturbations Landau damp and if $1/2< k\le1$ they do not.
The above dichotomy is a new phenomenon and highlights the importance of steady state regularity at the vacuum boundary in the discussion of long-time behaviour of the perturbations. Our proof of (nonquantitative) gravitational relaxation around steady states with $k>1$ is the first such result for the gravitational Vlasov-Poisson system. The key step in the proof is to show that no embedded eigenvalues exist in the essential spectrum of the linearised system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_07662 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Damping versus oscillations for a gravitational Vlasov-Poisson system Hadzic, Mahir Rein, Gerhard Schrecker, Matthew Straub, Christopher Analysis of PDEs Mathematical Physics 35Q83, 35Q85, 35P25, 35B40 We consider a family of isolated inhomogeneous steady states to the gravitational Vlasov-Poisson system with a point mass at the centre. They are parametrised by the polytropic index $k>1/2$, so that the phase space density of the steady state is $C^1$ at the vacuum boundary if and only if $k>1$. We prove the following sharp dichotomy result: if $k>1$ the linear perturbations Landau damp and if $1/2< k\le1$ they do not. The above dichotomy is a new phenomenon and highlights the importance of steady state regularity at the vacuum boundary in the discussion of long-time behaviour of the perturbations. Our proof of (nonquantitative) gravitational relaxation around steady states with $k>1$ is the first such result for the gravitational Vlasov-Poisson system. The key step in the proof is to show that no embedded eigenvalues exist in the essential spectrum of the linearised system. |
| title | Damping versus oscillations for a gravitational Vlasov-Poisson system |
| topic | Analysis of PDEs Mathematical Physics 35Q83, 35Q85, 35P25, 35B40 |
| url | https://arxiv.org/abs/2301.07662 |