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Damping versus oscillations for a gravitational Vlasov-Poisson system
- Publication Year :
- 2023
-
Abstract
- 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.<br />Comment: 49 pages, 1 figure
- Subjects :
- Mathematics - Analysis of PDEs
Mathematical Physics
35Q83, 35Q85, 35P25, 35B40
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2301.07662
- Document Type :
- Working Paper