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Well-posedness of the equation for the three-form field in eleven-dimensional supergravity


Author: Boris Ettinger
Journal: Trans. Amer. Math. Soc. 367 (2015), 887-910
MSC (2010): Primary 35L05; Secondary 83E50, 70S20
DOI: https://doi.org/10.1090/S0002-9947-2014-05900-X
Published electronically: September 26, 2014
MathSciNet review: 3280031
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Abstract: We analyze a semi-linear gauge-invariant wave equation which arises in the theory of supergravity. We prove that the Cauchy problem is well-posed globally in time for the fixed-gauge version of the equation for small compactly supported smooth data. We employ the method of Klainerman vector fields along with a finer analysis of the nonlinearity to establish an integrable decay in the energy estimate.


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Additional Information

Boris Ettinger
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Address at time of publication: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
Email: ettinger@math.berkeley.edu, ettinger@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-05900-X
Received by editor(s): May 20, 2011
Received by editor(s) in revised form: June 21, 2012
Published electronically: September 26, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.