GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM*

doi:10.1007/s10473-023-0113-8

Abstract

Abstract: The pointwise space-time behaviors of the Green's function and the global solution to the Vlasov-Poisson-Fokker-Planck (VPFP) system in three dimensional space are studied in this paper. It is shown that the Green's function consists of the diffusion waves decaying exponentially in time but algebraically in space, and the singular kinetic waves which become smooth for all $(t,x,v)$ when $t>0.$ Furthermore, we establish the pointwise space-time behaviors of the global solution to the nonlinear VPFP system when the initial data is not necessarily smooth in terms of the Green's function.

Key words: Vlasov-Poisson-Fokker-Planck system, Green's function, pointwise behavior, spectrum structure

Mingying zhong. GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*[J].Acta mathematica scientia,Series B, 2023, 43(1): 205-236.

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GREEN'S FUNCTION AND THE POINTWISE BEHAVIORS OF THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM^*

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