Asymptotic expansions for semilinear waves on asymptotically flat spacetimes
| Autor: | Looi, Shi-Zhuo, Xiong, Haoren |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. For cubic nonlinearities $a(t,x)\phi^3$, we prove $\phi(t, x) = 2c t^{-2} + O(t^{-3+})$ in compact spatial regions, with $c$ computable. For $a(t,x)\phi^p$ with $p \geq 4$, we show $\phi(t, x) = d t^{-3} + O(t^{-4+})$, extending Price's law to the nonlinear setting. Our approach combines radiation field analysis with a generalized low-energy resolvent expansion, providing a bridge between spectral and physical space methods. These results sharpen previous decay estimates and yield complete asymptotics across the entire spacetime, including black hole backgrounds. Comment: 48 pages |
| Databáze: | arXiv |
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