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 geq 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 Krieger Sterbenz Tataru which says that the most difficult part of Maxwell Dirac takes essentially the same form as Maxwell Klein Gordon

Global Well-posedness of High Dimensional Maxwell-dirac for Small Critical Data (Memoirs of the American Mathematical Society) PDF

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