Study of the Kramers-Fokker-Planck quadratic operator with a constant magnetic field

Abstract

We study the quadratic Kramers-Fokker-Planck operator with a constant magnetic field and with a quadratic potential. We describe the exact expression of the norm of the semi-group associated to the operator near the equilibrium. At this level, explicit and accurate estimates of this norm are shown in small and long times as well as uniform-in-time estimates when the magnetic parameter $b$ tends to infinity.

References in corpus (2)

• Spectral projections and resolvent bounds for partially elliptic quadratic differential operators
• Singular-value decomposition of solution operators to model evolution equations