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Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces

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arxiv 1404.1348 v2 pith:HB54XE55 submitted 2014-04-04 math.AP

classification math.AP
keywords equationsframeworkquasilineardevelopedkerr-desitterwaveadaptation
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We extend the semilinear framework developed by the two authors and the non-trapping quasilinear theory developed by the first author to solve quasilinear wave equations with normally hyperbolic trapping. The most well-known example that fits into our general framework is wave-type equations on Kerr-de Sitter space. The key advance is an adaptation of the Nash-Moser iteration to our framework.

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  1. On turbulence for spacetimes with stable trapping

    gr-qc 2024-11 conditional novelty 7.0 of 10

    On a fixed spacetime with stable trapping, the cubic wave equation produces a forward angular-mode cascade and growth of higher-order derivatives, behavior absent for linear waves.

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