Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

Article type: Research Article

Authors: Benedetto, Dario | Caglioti, Emanuele^{; *} | Rossi, Stefano

Affiliations: Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 2, 00185 Rome, Italy. E-mails: [email protected], [email protected], [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this “scattering problem”, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.

Keywords: Landau damping, HMF model, plasma echoes

DOI: 10.3233/ASY-211726

Journal: Asymptotic Analysis, vol. 129, no. 2, pp. 215-238, 2022