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PreprintarXiv licencearXiv

Long-time validity of the Korteweg-de Vries approximation for the Boussinesq equation

  • Younghun Hong
  • Junyeong Jang
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Abstract

We consider the Korteweg-de Vries (KdV) approximation for the good Boussinesq equation. Building upon the low-regularity local-in-time justification established by Hong and Yang \cite{HY2024}, we prove that this approximation remains valid on logarithmically long time intervals. The key ingredient is a persistence of regularity argument, which allows the local approximation to be iterated using the rescaled conservation law for the Boussinesq equation.

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Cite

BibTeXRIS
BibTeX
@misc{hong2026longtime,
  title = {{Long-time validity of the Korteweg-de Vries approximation for the Boussinesq equation}},
  author = {Younghun Hong and Junyeong Jang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30786},
  eprint = {2609.30786},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30786},
}
RIS
TY  - UNPB
TI  - Long-time validity of the Korteweg-de Vries approximation for the Boussinesq equation
AU  - Younghun Hong
AU  - Junyeong Jang
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.30786
UR  - https://arxiv.org/abs/2609.30786
AB  - We consider the Korteweg-de Vries (KdV) approximation for the good Boussinesq equation. Building upon the low-regularity local-in-time justification established by Hong and Yang \cite{HY2024}, we prove that this approximation remains valid on logarithmically long time intervals. The key ingredient is a persistence of regularity argument, which allows the local approximation to be iterated using the rescaled conservation law for the Boussinesq equation.
ER  -