The periodic kinetic Fokker-Planck equation homogenizes to an effective heat equation via second-order correctors, and its solutions admit large-scale approximations by heterogeneous polynomials with explicit errors.
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2026 2verdicts
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Nash-Aronson-type upper bounds are established for the fundamental solution of the linear kinetic Fokker-Planck equation with friction, Gaussian for long times reflecting velocity averaging and Kolmogorov-type for short times where friction is negligible.
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Large-Scale Regularity for the Periodic Kinetic Fokker-Planck equation
The periodic kinetic Fokker-Planck equation homogenizes to an effective heat equation via second-order correctors, and its solutions admit large-scale approximations by heterogeneous polynomials with explicit errors.
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Nash-Aronson Estimate for the Linear Kinetic Fokker-Planck equation
Nash-Aronson-type upper bounds are established for the fundamental solution of the linear kinetic Fokker-Planck equation with friction, Gaussian for long times reflecting velocity averaging and Kolmogorov-type for short times where friction is negligible.