Young-Pil Choi studied in this paper the existence and large time behaviour of solution to the following nonlinear Vlasov-Fokker-Planck equation

where and

Assuming the initial data close enough to the global Maxwellian

the author proved that the solution to the mentioned problem exists globally in the classical sense, and converges to the Maxwellian with an algebraic rate, i.e.

where

.

Moreover, if the spatial is periodic, then the convergence is exponential.

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Lecturer
School of Applied Mathematics and Informatics
Hanoi University of Science and Technology
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