Journal of the American Mathematical Society

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

Author(s): Matei Machedon; Jacob Sterbenz
Journal: J. Amer. Math. Soc. 17 (2004), 297-359.
MSC (2000): Primary 35Q60, 35L70
Posted: 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.

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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 35Q60, 35L70

Matei Machedon
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
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
Email: jks@math.umd.edu, sterbenz@math.princeton.edu

DOI: 10.1090/S0894-0347-03-00445-4
PII: S 0894-0347(03)00445-4
Received by editor(s): October 16, 2002
Posted: November 13, 2003
Additional Notes: Both authors were supported by NSF grant DMS-0100406.
Copyright of article: Copyright 2003, American Mathematical Society

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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