Sharp asymptotics for small data solutions of the Vlasov-Nordström system in three dimensions
- Author(s)
- Jérémie Joudioux, David Miro Fajman, Jacques Smulevici
- Abstract
This paper proves almost-sharp asymptotics for small data solutions of the Vlasov-Nordström system in dimension three. This system consists of a wave equation coupled to a transport equation and describes an ensemble of relativistic, self-gravitating particles. We derive sharp decay estimates using a variant of the vector-field method introduced in previous work. More precisely, we construct modified vector fields, depending on the solutions, to propagate L1-bounds for the distribution function and its derivatives. The modified vector fields are designed to have improved commutation properties with the transport operator and yet to still provide sufficient control on the solutions to allow for a sharp Klainerman-Sobolev type inequality. Our method does not require any compact support assumption in the velocity variable nor do we need strong interior decay for the solution to the wave equation.
- Organisation(s)
- Gravitational Physics, Department of Mathematics
- External organisation(s)
- Université Paris XI - Paris-Sud
- Publication date
- 2017
- Austrian Fields of Science 2012
- 101002 Analysis, 103028 Theory of relativity
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/sharp-asymptotics-for-small-data-solutions-of-the-vlasovnordstroem-system-in-three-dimensions(bcafbae6-6db0-4c78-88c8-55b6765348ad).html