| Abstract: |
| In this paper, we construct the global solutions near a local Maxwellian to the Vlasov-Poisson-Landau system with slab symmetry for the physical Coulomb interaction. The fluid quantities of this local Maxwellian are the approximate rarefaction wave solutions to the associated one-dimensional compressible Euler equations. We prove for the first time that for the Cauchy problem on this system, such a local Maxwellian is time asymptotically
stable under suitably small smooth perturbations and tend in large time to the rarefaction waves of the compressible Euler system with the corresponding Riemann data. As a byproduct, the nonlinear stability of the same rarefaction waves for the pure Landau equation is also proved. This illustrates in our setting that the electric field does not affect the propagation of rarefaction waves to the Landau equation. |
|