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

Xue Ping Wang

doi:10.1007/s00220-014-2273-9

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arXiv · 1403.0841

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

Xue Ping Wang

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Abstract

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.

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BibTeX RIS

Xue Ping Wang. 2014-03-31. Large-time asymptotics of solutions to the Kramers-Fokker-Planck equation with a short-range potential. https://doi.org/10.1007/s00220-014-2273-9

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