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

Ettinger, Boris

doi:10.1090/S0002-9947-2014-05900-X

Well-posedness of the equation for the three-form field in eleven-dimensional supergravity
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Trans. Amer. Math. Soc. 367 (2015), 887-910 Request permission

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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