Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces

Chen, Jingchun; He, Cong

doi:10.28919/cpr-pajm/1-17

Research article

Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces

Jingchun Chen, Cong He

Abstract

In this paper, we are concerned with the local well-posedness of the Vlasov-Poisson-Fokker-Planck equation near vacuum in the fractional Sobolev-Lebesgue space for the large initial data. To achieve this goal, we mainly adopt the energy method. In order to obtain the energy estimate, we establish an L²-L^q estimate related to the electronic term, and take advantage of the commutator estimates as well.

How to cite

J. Chen, C. He, Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces, Pan-Amer. J. Math. 1 (2022), 17. https://doi.org/10.28919/cpr-pajm/1-17

BibTeX

@article{Chen2022,
  author  = {Chen, Jingchun and He, Cong},
  title   = {Vlasov-Poisson-Fokker-Planck in Fractional Sobolev-Lebesgue Spaces},
  journal = {Pan-Amer. J. Math.},
  volume  = {1},
  year    = {2022},
  pages   = {17},
  doi     = {10.28919/cpr-pajm/1-17}
}