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PreprintarXiv licencearXiv

The Strauss conjecture for the wave equation with scattering damping

  • Elliot Adamson
  • Jason Metcalfe
  • Chengbo Wang
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Abstract

The focus of this article is to establish the existence portion of the Strauss conjecture for wave equations with spatially dependent scattering damping. In the current setting, the damping is not sufficiently strong to alter the critical Strauss exponent. In a subsequent study, the authors will consider the case of damping coefficients with critical decay where a shift of the Strauss exponent is expected. While several recent studies of the Strauss conjecture have relied upon weighted Strichartz estimates, here, instead, an approach that is based only on integrated local energy estimates, in particular those with both rp and ghost weights, is developed. This technique also applies to the problem for the free equation. Space-time Klainerman-Sobolev estimates provide the necessary decay to close the argument.

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Cite

BibTeXRIS
BibTeX
@misc{adamson2026strauss,
  title = {{The Strauss conjecture for the wave equation with scattering damping}},
  author = {Elliot Adamson and Jason Metcalfe and Chengbo Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14614},
  eprint = {2610.14614},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14614},
}
RIS
TY  - UNPB
TI  - The Strauss conjecture for the wave equation with scattering damping
AU  - Elliot Adamson
AU  - Jason Metcalfe
AU  - Chengbo Wang
PY  - 2026
DA  - 2026/10/10
PB  - arXiv
DO  - 10.48550/arxiv.2610.14614
UR  - https://arxiv.org/abs/2610.14614
AB  - The focus of this article is to establish the existence portion of the Strauss conjecture for wave equations with spatially dependent scattering damping. In the current setting, the damping is not sufficiently strong to alter the critical Strauss exponent. In a subsequent study, the authors will consider the case of damping coefficients with critical decay where a shift of the Strauss exponent is expected. While several recent studies of the Strauss conjecture have relied upon weighted Strichartz estimates, here, instead, an approach that is based only on integrated local energy estimates, in particular those with both r^p and ghost weights, is developed. This technique also applies to the problem for the free equation. Space-time Klainerman-Sobolev estimates provide the necessary decay to close the argument.
ER  -