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.
Quasimodes and a lower bound for the local energy decay of the Dirac equation in Schwarzschild-Anti-de Sitter spacetime
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abstract
We prove the existence of exponentially accurate quasimodes using the square of the Dirac operator on the Schwarzschild-Anti-de Sitter spacetime and the Agmon estimates. We then deduce a logarithmic lower bound for the local energy decay of the Dirac propagator.
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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.