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The Strauss conjecture for the wave equation with critical damping
Abstract
The Strauss conjecture concerns wave equations with power-type nonlinearities and seeks the optimal range of powers that admit global solutions for all sufficiently nice and sufficiently small initial data. In three spatial dimensions, it is well known that small data global existence is available provided that the power p>pc(3)=1+√2, where pc(n) denotes the critical power in n-spatial dimensions. In the current article, the analogous problem is considered for damped wave equations where the damping coefficient is at the critical scaling. When a denotes the constant multiple applied to the damping term, it is shown that the corresponding critical power is pc(3+a) provided that a is sufficiently small.
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BibTeX
@misc{adamson2026strauss,
title = {{The Strauss conjecture for the wave equation with critical damping}},
author = {Elliot Adamson and Jason Metcalfe and Chengbo Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14610},
eprint = {2610.14610},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14610},
}
RIS
TY - UNPB
TI - The Strauss conjecture for the wave equation with critical damping
AU - Elliot Adamson
AU - Jason Metcalfe
AU - Chengbo Wang
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14610
UR - https://arxiv.org/abs/2610.14610
AB - The Strauss conjecture concerns wave equations with power-type nonlinearities and seeks the optimal range of powers that admit global solutions for all sufficiently nice and sufficiently small initial data. In three spatial dimensions, it is well known that small data global existence is available provided that the power p>p_c(3)=1+√2, where p_c(n) denotes the critical power in n-spatial dimensions. In the current article, the analogous problem is considered for damped wave equations where the damping coefficient is at the critical scaling. When a denotes the constant multiple applied to the damping term, it is shown that the corresponding critical power is p_c(3+a) provided that a is sufficiently small.
ER -