at Google ScholarTitle data
Hadžić, Mahir ; Rein, Gerhard ; Schrecker, Matthew ; Straub, Christopher:
Damping Versus Oscillations for a Gravitational Vlasov–Poisson System.
In: Archive for Rational Mechanics and Analysis.
Vol. 249
(2025)
.
- 45.
ISSN 1432-0673
DOI: https://doi.org/10.1007/s00205-025-02114-y
Abstract in another language
We consider a family of isolated inhomogeneous steady
states of the gravitational Vlasov–Poisson system with a point mass at the centre. These are parametrised
by the polytropic index k > 1/2, so that the phase space density of the steady state is C1 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 ≤ 1 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 the 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 novelty of this work is the proof that no embedded eigenvalues exist in the essential spectrum of the linearised system.
Further data
| Item Type: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | gravitational Landau-damping; linear oscillations; Vlasov-Poisson system |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics > Professor Applied Mathematics - Univ.-Prof. Dr. Gerhard Rein Profile Fields > Advanced Fields > Nonlinear Dynamics |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 500 Science > 510 Mathematics |
| Date Deposited: | 01 Sep 2025 08:16 |
| Last Modified: | 01 Sep 2025 08:16 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/94556 |