Special Session 175: Modern Trends in Partial Differential Equations and General Relativity

On initial boundary value problems for the Maxwell-Schrodinger system
Takeshi Wada
Shimane University
Japan
Co-Author(s):    
Abstract:
In this talk, we study the initial-boundary value problem for the Maxwell-Schr\odinger equations (MS) in a bounded or exterior domain $\Omega\subset\R^d$, $d=2,3$, with smooth boundary $\partial\Omega$. MS is a system of the Schrodinger equation with electro-magnetic potentials and the Maxwell equations written in terms of electro-magnetic potentials. Physically, this system describes the interaction between a charged nonrelativistic quantum mechanical particle and the (classical) electromagnetic field generated by the motion of the particle. We will discuss the well-posedness of this system.