Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential

Xue Ping Wang (1)

1 Equations aux dérivées partielles

In this work, we use scattering method to study the Kramers-Fokker-Planck equation with a potential whose gradient tends to zero at the infinity. For short-range potentials in dimension three, we show that complex eigenvalues do not accumulate at low-energies and establish the low-energy resolvent asymptotics. This combined with high energy pseudospectral estimates valid in more general situations gives the large-time asymptotics of the solution in weighted $L^2$ spaces.

Mots clés: Time-decay; nonselfadjoint operators; Krammers-Fokker-Planck operators

Domaines: Théorie spectrale [math.SP]; Equations aux dérivées partielles [math.AP]

Xue Ping Wang. Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential. 2014. ⟨hal-00955484v3⟩