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Article contents
Scattering for critical wave equations with variable coefficients
Part of:
Hyperbolic equations and systems
Published online by Cambridge University Press: 30 April 2021
Abstract
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 $t\to \infty$
.
Keywords
MSC classification
Primary:
35L05: Wave equation
- Type
- Research Article
- Information
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
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