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The Cauchy problem for the classical Dirac-Klein-Gordon system in two spacedimensions is globally well-posed for L^2 Schoedinger data and wave data inH^{1/2} \times H^{-1/2}. In the case of smooth data there exists a globalsmooth (classical) solution. The proof uses function spaces of Bourgain typebased on Besov spaces - previously applied by Colliander, Kenig and Staffilanifor generalized Benjamin-Ono equations and also by Bejenaru, Herr, Holmer andTataru for the 2D Zakharov system - and the null structure of the systemdetected by d'Ancona, Foschi and Selberg, and a refined bilinear Strichartzestimate due to Selberg. The global existence proof uses an idea of Colliander,Holmer and Tzirakis for the 1D Zakharov system.

Global solutions for the Dirac-Klein-Gordon system in two space dimensions