A vector field method for relativistic transport equations with applications

Author(s)
David Fajman, Jeremie Joudioux, Jacques Smulevici
Abstract

We adapt the vector field method of Klainerman to the study of relativistic transport equations. First, we prove robust decay estimates for velocity averages of solutions to the relativistic massive and massless transport equations, without any compact support requirements (in x or v) for the distribution functions. In the second part of this article, we apply our method to the study of the massive and massless Vlasov- Nordström systems. In the massive case, we prove global existence and (almost) optimal decay estimates for solutions in dimensions n ≥ 4 under some smallness assumptions. In the massless case, the system decouples and we prove optimal decay estimates for the solutions in dimensions n ≥ 4 for arbitrarily large data, and in dimension 3 under some smallness assumptions, exploiting a certain form of the null condition satisfied by the equations. The 3-dimensional massive case requires an extension of our method and will be treated in future work.

Organisation(s)
Gravitational Physics
External organisation(s)
Université Paris XI - Paris-Sud
Journal
Analysis & PDE
Volume
10
Pages
1539-1612
No. of pages
74
ISSN
2157-5045
DOI
https://doi.org/10.2140/apde.2017.10.1539
Publication date
2017
Peer reviewed
Yes
Austrian Fields of Science 2012
103019 Mathematical physics
Keywords
ASJC Scopus subject areas
Analysis, Applied Mathematics, Numerical Analysis
Portal url
https://ucris.univie.ac.at/portal/en/publications/a-vector-field-method-for-relativistic-transport-equations-with-applications(7324243f-d205-4d0b-8c22-f871b0e71ac0).html