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.
Global analysis of quasilinear wave equations on asymptotically Kerr-de Sitter spaces
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abstract
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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2024 1verdicts
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On turbulence for spacetimes with stable trapping
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.