2022/08/30 by Shijie Dong, Dong, Shijie, Kuijie Li +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.2208.14131
On the (1+3) dimensional Minkowski spacetime, for small, regular initial data, it is well-known that the Dirac-Klein-Gordon system admits a global solution. In the present paper, we aim to establish the uniform boundedness of the total energy of the solution for this system. The proof relies on Klainerman's vector field and Alinhac's ghost weight methods. The main difficulty originates from the slow decay nature of the Dirac and wave components in three space dimensions. To overcome the difficulty, a sharp understanding of the structure for this system, and a new weighted conformal energy estimate are required. In addition, we also provide a few scattering results for the system.