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Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations

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Abstract

We study long-time dynamical behaviors of weakly self-consistent Vlasov–Fokker–Planck equations. We introduce Hessian matrix conditions on mean-field kernel functions, which characterizes the exponential convergence of solutions in \(L^1\) distances. The matrix condition is derived from the dissipation of a selected Lyapunov functional, namely auxiliary Fisher information functional. We verify proposed matrix conditions in examples.

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Correspondence to Qi Feng.

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Communicated by Anthony Bloch.

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E. Bayraktar is partially supported by the National Science Foundation under grant DMS-2106556 and by the Susan M. Smith chair. Q. Feng is partially supported by the National Science Foundation under grant DMS-2306769. W. Li is supported by AFOSR MURI FA9550-18-1-0502, AFOSR YIP award No. FA9550-23-1-0087, NSF RTG: 2038080, and NSF DMS-2245097.

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Bayraktar, E., Feng, Q. & Li, W. Exponential Entropy Dissipation for Weakly Self-Consistent Vlasov–Fokker–Planck Equations. J Nonlinear Sci 34, 7 (2024). https://doi.org/10.1007/s00332-023-09984-0

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