Sigmund Selberg

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We prove global well-posedness below the charge norm (i.e., the L 2 norm of the Dirac spinor) for the Dirac-Klein-Gordon system of equations (DKG) in one space dimension. Adapting a method due to Bourgain, we split off the high frequency part of the initial data for the spinor, and exploit nonlinear smoothing effects to control the evolution of the high(More)
We prove a quadrilinear integral estimate in space-time for solutions of the homogeneous wave equation on R 1+2. This estimate is a generalization of a previously known bilinear L 2 estimate, and it arises naturally in the study of the local regularity properties of a hyperbolic model equation connected with wave maps from Minkowski space R 1+2 into a(More)
We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T ]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two(More)
We prove that the Maxwell-Klein-Gordon system on R 1þ4 relative to the Coulomb gauge is locally well-posed for initial data in H 1þ" for all " > 0. This builds on previous work by Klainerman and Machedon [6] who proved the corresponding result, with the additional restriction of small-norm data, for a model problem obtained by ignoring the elliptic features(More)
We extend recent results of S. Machihara and H. Pecher on low regularity well-posedness of the Dirac-Klein-Gordon (DKG) system in one dimension. Our proof, like that of Pecher, relies on the null structure of DKG, recently completed by D'Ancona, Foschi and Selberg, but we show that in 1d the argument can be simplified by modifying the choice of projections(More)
We prove that in the nonrelativistic limit c → ∞, where c is the speed of light, solutions of the Klein-Gordon-Maxwell system on R 1+3 converge in the energy space C([0, T]; H 1) to solutions of a Schrödinger-Poisson system, under appropriate conditions on the initial data. This requires the splitting of the scalar Klein-Gordon field into a sum of two(More)