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

Klainerman, Sergiu; Tataru, Daniel

doi:10.1090/S0894-0347-99-00282-9

On the optimal local regularity for the Yang-Mills equations in $\mathbb {R}^{4+1}$
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by Sergiu Klainerman and Daniel Tataru

J. Amer. Math. Soc. 12 (1999), 93-116

DOI: https://doi.org/10.1090/S0894-0347-99-00282-9

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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 $\mathbb {R}^{n+1}$, for the case of the critical dimension $n=4$. 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.

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