Local well-posedness of the coupled Yang-Mills and Dirac system for low regularity data

Abstract

We consider the classical Yang-Mills system coupled with a Dirac equation in 3+1 dimensions. Using that most of the nonlinear terms fulfill a null condition we prove local well-posedness for data with minimal regularity assumptions. This problem for smooth data was solved forty years ago by Y. Choquet-Bruhat and D. Christodoulou. Our result generalizes a similar result for the Yang-Mills equation by S. Selberg and A. Tesfahun.

24 pages. The proof of one of the bilinear estimates was corrected

References in corpus (1)

• Finite energy global well-posedness of the Yang-Mills equations on ${\mathbb{R}}^{1+3}$: An approach using the Yang-Mills heat flow