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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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

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
  • MR Author ID: 102350
  • Daniel Tataru
  • Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
  • MR Author ID: 267163
  • 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.
  • © Copyright 1999 American Mathematical Society
  • 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