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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
DOI: https://doi.org/10.1090/S0894-0347-99-00282-9
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 $n=4$. 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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Additional Information

Sergiu Klainerman
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

Daniel Tataru
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544

DOI: https://doi.org/10.1090/S0894-0347-99-00282-9
Keywords: Yang-Mills, well-posedness, regularity, Strichartz
Received by editor(s): April 1, 1997
Received by editor(s) in revised form: March 3, 1998
Additional Notes: The first author’s research was partially supported by NSF grant DMS-9400258.
The second author’s research was partially supported by NSF grant DMS-9622942 and by an Alfred P. Sloan fellowship.
Article copyright: © Copyright 1999 American Mathematical Society

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