Abstract
AbstractWe consider the classical Yang–Mills system coupled with a Dirac equation in 3+1 dimensions in temporal gauge. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for small data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Y. Choquet-Bruhat and D. Christodoulou. The corresponding problem in Lorenz gauge was considered recently by the author in [14].
Funder
Bergische Universität Wuppertal
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. d’Ancona, P., Foschi, D., Selberg, S.: Atlas of products for wave-Sobolev spaces on $$\mathbb{R}^{1+3}$$. Trans. Am. Math. Soc. 364, 31–63 (2012)
2. d’Ancona, P., Foschi, D., Selberg, S.: Null structure and almost optimal regularity for the Dirac–Klein–Gordon system. J. Eur. Math. Soc. 9, 877–899 (2007)
3. Choquet-Bruhat, Y., Christodoulou, D.: Existence of global solutions of the Yang–Mills, Higgs and spinor field equations in 3 + 1 dimensions. Annales Scientifiques de l’É.N.S. 4e série 14(4), 481–506 (1981)
4. Ginibre, J., Velo, G.: Generalized Strichartz inequalities for the wave equation. J. Funct. Anal. 133, 60–68 (1995)
5. Huh, H., Oh, S.-J.: Low regularity solutions to the Chern–Simons–Dirac and the Chern–Simons–Higgs equations in the Lorenz gauge. Commun. Partial Differ. Equ. 41, 375–397 (2016)