2009/03/18 by Axel Gruenrock, Gruenrock, Axel, Hartmut Pecher +1
Mathematics · #35L70 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L70 #msc:35Q55
paper · pdf · doi:10.48550/arxiv.0903.3189
22 pages
arxiv created 2009/06/22 · arxiv updated 2009/12/01
The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L2 Schoedinger data and wave data in H1/2 × H-1/2. In the case of smooth data there exists a global smooth (classical) solution. The proof uses function spaces of Bourgain type based on Besov spaces - previously applied by Colliander, Kenig and Staffilani for generalized Benjamin-Ono equations and also by Bejenaru, Herr, Holmer and Tataru for the 2D Zakharov system - and the null structure of the system detected by d'Ancona, Foschi and Selberg, and a refined bilinear Strichartz estimate due to Selberg. The global existence proof uses an idea of Colliander, Holmer and Tzirakis for the 1D Zakharov system.