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

We analyze the equations for the three-form field - a system of semi-linear gauge-invariant wave equations which arises in the theory of eleven dimensional supergravity. We prove that the Cauchy problem is well-posed globally in time for the fixed-gauge version of the equation for a 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.

preprint2011arXivOpen access
Boris Ettinger
math.AP
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Boris Ettinger

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