A vector field method for relativistic transport equations with applications

David Fajman (Korresp. Autor*in), Jeremie Joudioux, Jacques Smulevici

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

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.

OriginalspracheEnglisch
Seiten (von - bis)1539-1612
Seitenumfang74
FachzeitschriftAnalysis & PDE
Jahrgang10
Ausgabenummer7
DOIs
PublikationsstatusVeröffentlicht - 2017

ÖFOS 2012

  • 103019 Mathematische Physik

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