We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
A second look at the Kurth solution in galactic dynamics.
- Authors
Kunze, Markus
- Abstract
The Kurth solution is a particular non-isotropic steady state solution to the gravitational Vlasov-Poisson system. It has the property that by means of a suitable time-dependent transformation it can be turned into a family of time-dependent solutions. Therefore, for a general steady state [Math Processing Error] Q (x , v) = Q ~ (e Q , β) , depending upon the particle energy [Math Processing Error] e Q and [Math Processing Error] β = ℓ 2 = | x ∧ v | 2 , the question arises if solutions [Math Processing Error] f could be generated that are of the form [Math Processing Error] f (t) = Q ~ (e Q (R (t) , P (t) , B (t)) , B (t)) for suitable functions [Math Processing Error] R , [Math Processing Error] P and [Math Processing Error] B , all depending on [Math Processing Error] (t , r , p r , β) for [Math Processing Error] r = | x | and [Math Processing Error] p r = x ⋅ v | x |. We are going to show that, under some mild assumptions, basically if [Math Processing Error] R and [Math Processing Error] P are independent of [Math Processing Error] β , and if [Math Processing Error] B = β is constant, then [Math Processing Error] Q already has to be the Kurth solution. This paper is dedicated to the memory of Professor Robert Glassey.
- Subjects
GALACTIC dynamics; MATHEMATICS
- Publication
Kinetic & Related Models, 2022, Vol 15, Issue 4, p651
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2021028