Parametrix for wave equations on a rough background III : space-time regularity of the phase - Laboratoire Jacques-Louis Lions Accéder directement au contenu
Article Dans Une Revue Asterisque Année : 2018

Parametrix for wave equations on a rough background III : space-time regularity of the phase

Jeremie Szeftel

Résumé

This is the third of a sequence of four papers [21], [22], [23], [24] dedicated to the construction and the control of a parametrix to the homogeneous wave equation g φ = 0, where g is a rough metric satisfying the Einstein vacuum equations. Controlling such a parametrix as well as its error term when one only assumes L 2 bounds on the curvature tensor R of g is a major step of the proof of the bounded L 2 curvature conjecture proposed in [12], and solved by S. Klainerman, I. Rodnianski and the author in [17]. On a more general level, this sequence of papers deals with the control of the eikonal equation on a rough background, and with the derivation of L 2 bounds for Fourier integral operators on manifolds with rough phases and symbols, and as such is also of independent interest.
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Dates et versions

hal-02410634 , version 1 (21-01-2020)

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Jeremie Szeftel. Parametrix for wave equations on a rough background III : space-time regularity of the phase. Asterisque, 2018, 401, ⟨10.24033/ast.1051⟩. ⟨hal-02410634⟩
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