A SECOND LOOK AT THE KURTH SOLUTION IN GALACTIC DYNAMICS - Kölner UniversitätsPublikationsServer

Kunze, Markus . A SECOND LOOK AT THE KURTH SOLUTION IN GALACTIC DYNAMICS. Kinet. Relat. Mod.. SPRINGFIELD: AMER INST MATHEMATICAL SCIENCES-AIMS. ISSN 1937-5077

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DOI:10.3934/krm.2021028

Abstract

The Kurth solution is a particular non-isotropic steady state so-lution 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 fam-ily of time-dependent solutions. Therefore, for a general steady state Q(x, v) = (Q) over tilde (e(Q), beta), depending upon the particle energy e(Q) and beta = l(2) = vertical bar x boolean AND v vertical bar(2), the question arises if solutions f could be generated that are of the form f(t) = (Q) over tilde (e(Q), (R(t), P(t), B(t)), B(t)) for suitable functions R, P and B, all depending on (t, r, p(r), beta) for r = vertical bar x vertical bar and pr = x center dot v/vertical bar x vertical bar. 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.

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