|
|||||
 |
|
|
|
|
A vector field method
for relativistic transport equations with applications
David Fajman, Jérémie Joudioux and Jacques Smulevici |
|
Vol. 10 (2017), No. 7, 1539–1612
|
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 or ) 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 under some smallness assumptions. In the massless case, the system decouples and we prove optimal decay estimates for the solutions in dimensions for arbitrarily large data, and in dimension under some smallness assumptions, exploiting a certain form of the null condition satisfied by the equations. The -dimensional massive case requires an extension of our method and will be treated in future work. |
Keywords
relativistic kinetic equations, wave equation, vector-field
method, asymptotic behaviour, nonlinear stability,
Vlasov–Nordström system
|
Mathematical Subject Classification 2010
Primary: 35B40, 35Q83, 83C30
|
Milestones
Received: 28 April 2016
Revised: 13 April 2017
Accepted: 9 May 2017
Published: 1 August 2017
|
Authors |
| David Fajman | |
| Gravitational Physics Faculty of Physics University of Vienna Boltzmanngasse 5 1090 Vienna Austria |
|
| Jérémie Joudioux | |
| Gravitational Physics Faculty of Physics University of Vienna Boltzmanngasse 5 1090 Vienna Austria |
|
| Jacques Smulevici | |
| Laboratoire de Mathématiques Université Paris-Sud 11 Bât. 425 91405 Orsay Cedex France |
|
|
