Asymptotic stability for the Dirac–Klein–Gordon system in two space dimensions
Shijie Dong
Southern University of Science and Technology, Shenzhen, ChinaZoe Wyatt
University of Cambridge, United Kingdom
Abstract
We study the Dirac–Klein–Gordon system in 1 + 2 spacetime dimensions. We show global existence of solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result for the Dirac–Klein–Gordon system in 1 + 2 spacetime dimensions in the case of a massive Klein–Gordon field and a massless Dirac field. The nonlinearities are below critical in two spatial dimensions, and so our method requires the identification of special structures within the system and novel weighted energy estimates. Another key advance is that our proof allows us to weaken certain conditions on the nonlinear structures that have been assumed in the literature.
Cite this article
Shijie Dong, Zoe Wyatt, Asymptotic stability for the Dirac–Klein–Gordon system in two space dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 6, pp. 1419–1464
DOI 10.4171/AIHPC/103