2023/10/13 by Moreno, Matias
Engineering · Mathematics · Physics and Astronomy · #35Q83 (Primary) 35Q85 (Secondary) #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2310.09351
openalex publication_date 2023/10/13 · openalex created_date 2023/10/18 · openalex updated_date 2026/07/28
We study a Newtonian model which allows us to describe some extremely flat objects in galactic dynamics. This model is described by a partial differential equation system called Vlasov-Poisson, whose solutions describe the temporal evolution of a collisionless particle system in the phase space, subject to a self interacting gravitational potential. We treat the Flat VlasovPoisson system with an external gravitational potential induced by a fixed mass density. The aim of this article is the study of the existence, regularity, and stability of steady states solutions of the Flat Vlasov-Poisson system in this case. We solved a variational problem to find minimizers for the Casimir-Energy functional in a suitable set of functions. The minimization problem is solved through a reduction of the original optimization problem with a scheme used in [FR06], but instead of a concentration-compactness argument, we use a symmetrization argument to construct a spherically symmetric solution for the reduced problem. It was proven that this minimizer induces a solution for the original minimization problem. The regularity of the gravitational potential was also obtained, implying that the solutions are steady states of the Flat Vlasov-Poisson system. The minimization problem also works as a key to give us a similar non-linear stability result.