Stationary and static stellar dynamic models with axial symmetry

1998/06/10 by Gerhard Rein
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.MP #msc:35Q99 #msc:85A05 #msc:85A15

paper · pdf

published as Nonlinear Analysis 41, 313 - 344 (2000) · 38 pages, Latex

arxiv created 1998/06/10 · arxiv updated 2009/11/30

Abstract

We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry. Using the implicit function theorem we show that certain stationary, spherically symmetric solutions can be embedded in one parameter families of stationary, axially symmetric solutions with finite radius and finite mass. In general, these new steady states have non-vanishing average velocity field, but they can also be constructed such that their velocity field does vanish, in which case they are called static.

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