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Scattering for critical wave equations with variable coefficients
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 2 / May 2021
- Published online by Cambridge University Press:
- 30 April 2021, pp. 298-316
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- Article
- Export citation
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We prove that solutions to the quintic semilinear wave equation with variable coefficients in ${{\mathbb {R}}}^{1+3}$
scatter to a solution to the corresponding linear wave equation. The coefficients are small and decay as $|x|\to \infty$
, but are allowed to be time dependent. The proof uses local energy decay estimates to establish the decay of the $L^{6}$
norm of the solution as $t\to \infty$
.
