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 global solutions 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
