On the optimal local regularity for the Yang-Mills equations in ℝ⁴⁺¹

Abstract

The aim of the paper is to develop the Fourier Analysis techniques needed in the study of optimal well-posedness and global regularity properties of the Yang-Mills equations in Minkowski space-time R n + 1 \mathbb {R}^{n+1} , for the case of the critical dimension n = 4 n=4 . We introduce new functional spaces and prove new bilinear estimates for solutions of the homogeneous wave equation, which can be viewed as generalizations of the well-known Strichartz-Pecher inequalities.