Local well-posedness of the two-dimensional Dirac-Klein-Gordon equations\n in Fourier-Lebesgue spaces

2019/10/09 by Hartmut Pecher, Pecher, Hartmut
Engineering · Mathematics · #35L70 #35Q40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1910.03972

openalex publication_date 2019/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The local well-posedness problem is considered for the Dirac-Klein-Gordon\nsystem in two space dimensions for data in Fourier-Lebesgue spaces\n\H^s,r , where \‖f\‖_\H^s,r = \‖ \⟨ \ξ \⟩^s\n\f\‖_L^r' and r and r' denote dual exponents. We lower the\nregularity assumptions on the data with respect to scaling improving the\nresults of d'Ancona, Foschi and Selberg in the classical case r=2 . Crucial\nis the fact that the nonlinearities fulfill a null condition as detected by\nthese authors.\n

Related

• Unconditional well-posedness for the Dirac - Klein - Gordon system in two space dimensions
• Almost optimal local well-posedness for the Maxwell-Klein-Gordon system\n with data in Fourier-Lebesgue spaces
• Local well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions
• Low regularity well-posedness for the one-dimensional Dirac - Klein - Gordon system
• Local well-posedness for the nonlinear Dirac equation in two space dimensions