A vector field method for relativistic transport equations with applications

Autor(en)

David Fajman, Jeremie Joudioux, Jacques Smulevici

Abstrakt

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(en)

Gravitationsphysik

Externe Organisation(en)

Université Paris XI - Paris-Sud

Journal

Analysis & PDE

Band

10

Seiten

1539-1612

Anzahl der Seiten

74

ISSN

2157-5045

DOI

https://doi.org/10.2140/apde.2017.10.1539

Publikationsdatum

2017

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Analysis, Applied Mathematics, Numerical Analysis

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/7324243f-d205-4d0b-8c22-f871b0e71ac0