The Vlasov-Poisson equation in ${\mathbb{R}}^3$ with infinite charge and velocities

Abstract

We consider the Vlasov-Poisson equation in ${\mathbb{R}}^3$ with initial data which are not $L^1$ in space and have unbounded support in the velocities. Assuming for the density a slight decay in space and a strong decay in velocities, we prove existence and uniqueness of the solution, thus generalizing the analogous result given in [5] for data compactly supported in the velocities.

References in corpus (1)

• A Vlasov-Poisson plasma with unbounded mass and velocities confined in a cylinder by a magnetic mirror

Cited by in corpus (2)

• Time evolution of a Vlasov-Poisson plasma with different species and infinite mass in ${\mathbb{R}}^3$
• Efficacy of a magnetic shield against a Vlasov-Poisson plasma