Global well-posedness of high dimensional Maxwell-Dirac for small critical data - Gavrus, Cristian (Cristian Dan); Oh, Sung-Jin (Memoirs of the American Mathematical Society, 2020)
In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on \mathbb{R}^{1+d} (d≥ 4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' 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 Kri.