Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1

Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We consider the abstract scattering structure of the non homogeneous linearized Vlasov-Poisson equations from the viewpoint of trace class properties which are emblematic of the abstract scattering theory [13, 14, 15, 19]. In dimension 1+1, we derive an original reformulation which is trace class. It yields the existence of the Moller wave operators. The non homogeneous background electric field is periodic with 4 + ε bounded derivatives. Mathematics Subject Classification (2010). Primary: 47A40; Secondary: 35P25.

Mots clés: Trace class; linear Vlasov-Poisson; wave operators

Domaines: Théorie spectrale [math.SP]; Physique mathématique [math-ph]

Bruno Després. Trace class properties of the non homogeneous linear Vlasov-Poisson equation in dimension 1+1. Journal of Spectral Theory, 2021, 11 (2). ⟨hal-02366266⟩