Hongjie Dong, Brown University

The main impetus for plasma studies is nuclear fusion, with tokamak serving as a key device that confines charged particles within a toroidal boundary in the presence of a magnetic field. The relativistic Vlasov-Maxwell-Landau system is a fundamental model, describing the evolution of charged particles under the combined effects of electromagnetic forces and collisions. In this talk, I will present joint work with Yan Guo and Timur Yastrzhembskiy on this system in a general three-dimensional domain. We consider physically natural boundary conditions: particles are specularly reflected at the boundary, while the electromagnetic field satisfies the perfectly conducting boundary condition.
We establish a global well-posedness theory for solutions near equilibrium and prove their stability as time tends to infinity. I will begin with a brief introduction to the model and its physical meaning, and then explain some of the main mathematical difficulties arising from the coupling of particle transport, collisions, electromagnetic fields, and boundary effects. The talk will be accessible without any background in plasma physics or partial differential equations.