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.