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

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ISSN 1088-6834(online) ISSN 0894-0347(print)

On the optimal local regularity
for the Yang-Mills equations in $\mathbb{R}^{4+1}$

Authors: Sergiu Klainerman and Daniel Tataru
Journal: J. Amer. Math. Soc. 12 (1999), 93-116
MSC (1991): Primary 58E15, 35B65, 35Q40
MathSciNet review: 1626261
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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 . 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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