Propagation of Velocity Moments for the Magnetized Vlasov-Poisson System with Space-Time Dependent Magnetic Fields

TL;DR

This paper proves that velocity moments of solutions to the magnetized Vlasov-Poisson system with space-time dependent magnetic fields remain finite over time, ensuring global solutions and stability similar to unmagnetized cases.

Contribution

It establishes the propagation of velocity moments and regularity for the magnetized Vlasov-Poisson system with space-time dependent magnetic fields, leading to global existence results.

Findings

Velocity moments remain finite for all times.

Existence of global classical solutions is proved.

Optimal stability estimates in kinetic-Wasserstein distance are established.

Abstract

We prove that polynomial velocity moments of solutions to the 2D magnetized Vlasov-Poisson system and the 3D magnetized screened Vlasov-Poisson equation remain finite for all times, provided they are finite initially, even when the external magnetic field $B=B(t,x)$ is space-time dependent. We deduce propagation of regularity, thereby implying the existence of global classical solutions. Moreover, we prove optimal stability estimates in the kinetic-Wasserstein distance on par with the unmagnetised case.