Tuesday, May 29, 2018 - 11:00 in V2-210/216
Global well-posedness of the high dimensional Maxwell-Dirac equation for small critical data
A talk in the Keine Reihe series by
Cristian Gavrus from University of California, Berkeley
| Abstract: |
We discuss the global well-posedness of the massless Maxwell-Dirac equation in Coulomb gauge on $\mathbb{R}^{1+d}$ ($d\geq 4$) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of our proof are A) uncovering null structure of Maxwell-Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell-Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru), which says that the most difficult part of Maxwell-Dirac takes essentially the same form as Maxwell-Klein-Gordon. We will also discuss the massive case. This is joint work with Sung-Jin Oh.
|
Back
