# American Institute of Mathematical Sciences

doi: 10.3934/krm.2021028
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## A second look at the Kurth solution in galactic dynamics

 Universität Köln, Institut für Mathematik, Weyertal 86-90, D-50931 Köln, Germany

Received  March 2021 Revised  June 2021 Early access August 2021

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
 $Q(x, v) = \tilde{Q}(e_Q, \beta)$
, depending upon the particle energy
 $e_Q$
and
 $\beta = \ell^2 = |x\wedge v|^2$
, the question arises if solutions
 $f$
could be generated that are of the form
 $f(t) = \tilde{Q}\Big(e_Q(R(t), P(t), B(t)), B(t)\Big)$
for suitable functions
 $R$
,
 $P$
and
 $B$
, all depending on
 $(t, r, p_r, \beta)$
for
 $r = |x|$
and
 $p_r = \frac{x\cdot v}{|x|}$
. We are going to show that, under some mild assumptions, basically if
 $R$
and
 $P$
are independent of
 $\beta$
, and if
 $B = \beta$
is constant, then
 $Q$
already has to be the Kurth solution.
This paper is dedicated to the memory of Professor Robert Glassey.
Citation: Markus Kunze. A second look at the Kurth solution in galactic dynamics. Kinetic & Related Models, doi: 10.3934/krm.2021028
##### References:

show all references