Online talk

In this talk, I will discuss the Vlasov-Poisson-Landau system in a bounded domain with the specular-reflection boundary condition. This is a classical model for a dilute collisional plasma interacting through Coulombic collisions and self-generated electric fields. We establish the global well-posedness for small initial perturbations near the Maxwellian equilibrium state. The proof is based on a new improved $L^{2}\rightarrow L^{\infty}$ framework: $L^{2}$ energy estimate combines with the $S^{p}$ estimate for ultra-parabolic equations. 

This talk is based on the joint work with Hongjie Dong and Yan Guo.