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Large-Time Asymptotics of Solutions to the Kramers-Fokker-Planck Equation with a Short-Range Potential

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Abstract

In this work, we use a 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 obtain the low-energy resolvent asymptotics. This, combined with high energy pseudospectral estimates valid in more general situations, gives the large-time asymptotics of solutions in weighted L 2 spaces.

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Authors and Affiliations

  1. Laboratoire de Mathématiques Jean Leray, UMR CNRS 6629, Université de Nantes, 44322, Nantes Cedex 3, France

    Xue Ping Wang

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  1. Xue Ping Wang
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Correspondence to Xue Ping Wang.

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Communicated by C. Mouhot

Research supported in part by French ANR Project NOSEVOL BS01019 01 and by Chinese Qian Ren programme at Nanjing University.

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Wang, X.P. Large-Time Asymptotics of Solutions to the Kramers-Fokker-Planck Equation with a Short-Range Potential. Commun. Math. Phys. 336, 1435–1471 (2015). https://doi.org/10.1007/s00220-014-2273-9

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  • DOI: https://doi.org/10.1007/s00220-014-2273-9

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