## Almost optimal local well-posedness for the (3+1)-dimensional Maxwell–Klein–Gordon equations

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- by Matei Machedon and Jacob Sterbenz
- J. Amer. Math. Soc.
**17**(2004), 297-359 - DOI: https://doi.org/10.1090/S0894-0347-03-00445-4
- Published electronically: November 13, 2003
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## Abstract:

We prove that the evolution problem for the Maxwell–Klein– Gordon system is locally well posed when the initial data belong to the Sobolev space $H^{\frac {1}{2} + \epsilon }$ for any $\epsilon > 0$. This is in spite of a complete failure of the standard model equations in the range $\frac {1}{2} < s < \frac {3}{4}$. The device that enables us to obtain inductive estimates is a new null structure which involves cancellations between the elliptic and hyperbolic terms in the full equations.## References

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## Bibliographic Information

**Matei Machedon**- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- MR Author ID: 117610
- Email: mxm@math.umd.edu
**Jacob Sterbenz**- Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
- Address at time of publication: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
- MR Author ID: 733516
- Email: jks@math.umd.edu, sterbenz@math.princeton.edu
- Received by editor(s): October 16, 2002
- Published electronically: November 13, 2003
- Additional Notes: Both authors were supported by NSF grant DMS-0100406.
- © Copyright 2003 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**17**(2004), 297-359 - MSC (2000): Primary 35Q60, 35L70
- DOI: https://doi.org/10.1090/S0894-0347-03-00445-4
- MathSciNet review: 2051613