Vlasov-Poisson-Landau System with Specular-Reflection Boundary Condition
Time: 2020-11-30
Published By: He Liu
Speaker(s): Zhimeng Ouyang (Brown University)
Time: 10:00-11:00 December 16, 2020
Venue: Online
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near the Maxwellian equilibrium state with decay in time and some regularity results for small initial perturbations, in any general bounded domain (including a torus as in a tokamak device), in the presence of specular-reflection boundary condition. We provide a new improved $L^{2}\rightarrow L^{\infty}$ framework: $L^{2}$ energy estimate combines only with $S_{\mathcal{L}}^{p}$ estimate for the ultra-parabolic equation.
This talk is based on the joint work with Hongjie Dong and Yan Guo.
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