Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition
We study the timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition. Given a global solution u to the scalar wave equation with sufficiently small $C_c^\infty $ initial data, we derive an asymptotic formula for this global solution i...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2025-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509425100728/type/journal_article |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We study the timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition. Given a global solution u to the scalar wave equation with sufficiently small
$C_c^\infty $
initial data, we derive an asymptotic formula for this global solution inside the light cone (i.e. for
$|x|<t$
). It involves the scattering data obtained in the author’s asymptotic completeness result in [75]. Using this asymptotic formula, we prove that u must vanish under some decaying assumptions on u or its scattering data, provided that the wave equation violates the null condition. |
|---|---|
| ISSN: | 2050-5094 |