The 3D Vlasov-Poisson-Landau System Near 1D Local Maxwellians

摘要

We consider the Cauchy problem on the Vlasov-Poisson-Landau system with the Coulomb interaction in the three dimensional space domain RxT2. Although there have been extensive studies on global existence and large time behavior of solutions near global Maxwellians either in T3 or R3, it is unknown whether solutions can be constructed around some non-trivial asymptotic profiles. In this paper, we obtain the global solutions near a spatially one-dimensional local Maxwellian connecting two distinct global Maxwellians at x1=+/- infinity, where the fluid components of the local Maxwellian are the smooth approximate rarefaction wave of the corresponding full compressible Euler system in x1 is an element of R. We also prove the large time asymptotics of global solutions towards such planar rarefaction waves, and establish the propagation of the high-order moments and regularity of solutions with large amplitude. As a byproduct, all these results can be carried over to the pure Landau equation in the same setting.