Decay estimates of solutions to the N‐species Vlasov–Poisson system with small initial data

Abstract

This paper is concerned with the time decay rates of the N−species Vlasov–Poisson system with small data in the whole space. The global existence and large time behaviors are obtained in ℝ3 and more higher dimensional space. For the proof, the classical (for ℝn, n ≥ 4) and the modified (for ℝ3) vector field method and the bootstrap argument are mainly employed. Compared to the unipolar case, there are some crucial new ideas introduced to handle the multi‐species case, such as a new bootstrap assumption with some necessary parameters and the multipolar version of vector field method with new coefficients corresponding to different species charged particles, respectively.