ABSTRACT

The Vlasov-Poisson-Boltzmann system is a mathematical model used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the Boltzmann operator instead of the classical Landau operator with the Coulomb potential. The perturbation theory of such system around global Maxwellians recently has been well established since Guo founded his robust energy method in 2002. It is then interesting to further study the existence and stability of nontrivial large time asymptotic profiles for the system even with slab symmetry in space, particularly understanding the nontrivial electric potential as well as its effect on the long-term dynamics of the self-consistent system. In this talk, I will discuss a recent result with Shuangqian Liu on the study of the problem in the setting of rarefaction waves. The analytical tool is based on the macro-micro decomposition by Liu-Yang-Yu that we can be able to develop into the case for the two-species Boltzmann equations around local bi-Maxwellians. Our focus is to explain how the disparate masses and charges of particles play a role in the stability analysis.

[Light refreshments will be served outside the venue at 4:00-4:30 pm. Please come and join us.]