CUNY Graduate Center Differential Geometry Seminar presents

Maxwell-Klein-Gordon Equations in 4-dimensional Minkowski Space

Maria Psarelli

Bronx Community College, C.U.N.Y.

Wednesday, March 21

2:45-3:45 pm, Room 4419

This talk will focus on the asymptotic behavior of the solutions of massive coupled Maxwell-Klein-Gordon equations. The problem belongs in the area of nonlinear systems of hyperbolic equations and abelian gauge field theory. The presence of charge in the initial data together with the mass term in the Klein-Gordon equation results in new issues that cannot be accomodated by standard methods such as the conformal transformation. A covariant Lie derivative operator for the Klein-Gordon field is introduced and allows us to take care of the most troublesome terms in the error estimates. The proof is based on gauge invariant Lie derivative energy estimates and geometric properties of the fields equations.