Stability of flat galaxies [Elektronische Ressource] / von Roman Fiřt

Stability of flat galaxiesBei der Universit¨at Bayreuthzur Erreichung des Grades einesDoktors der Naturwissenschaften (Dr.rer.nat.)vorgelegte AbhandlungvonRoman Fiˇrtgeboren am 02.Dezember 1980 in Ostrava1. Gutachter:2. Gutachter:Tag der Einreichung:Tag des Kolloquiums:I would like to give my personal thanks to Prof. Dr. Gerhard Rein for introducing thisinteresting topic to me and for his guidance through my graduate studies. I would alsolike to thank Dipl.-Math. Achim Schulze and Dipl.-Math. Martin Seehafer for countlessfruitfull discussions.ContentsAbstract vNotation vii1 Introduction 12 The flat Vlasov–Poisson system 72.1 Disk-like galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 2D kinematics + 3D potential . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Stability via reduction 113.1 Energy–Casimir functionals and reduction . . . . . . . . . . . . . . . . . . . 123.2 Existence of a solution to the reduced variational problem . . . . . . . . . . 173.3 Stability of minimizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 Connection to the Euler–Poisson system . . . . . . . . . . . . . . . . . . . . 254 The Kuzmin disk 274.1 Existence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Existence and stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Flat galaxies with dark matter halos 455.1 Motivation . . . . . . . . . . . . . . . . . .