## 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.## References

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## Bibliographic 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