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Initial and initial-boundary value problems for a cubic sixth-order Boussinesq equation

  • Yuhao Xie
  • Shenghao Li
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Abstract

In this paper, we consider the sixth-order Boussinesq equation with a cubic nonlinearity, utt−uxx+k uxxxx−uxxxxxx+( u3 ) xx=0, with k=± 1, posed on both ℝ+ and ℝ. The local wellposedness are improved in related Bourgain-type spaces, Xs,b, for s>−1/2 with b=1/2 and b>1/2 accordingly (See. \cite{esfahani2025well,zhong2024local}). The key ingredient is to refine the trilinear estimate on Burgain type space by adapting ideas from Tao's multiplier method, interpolation theory and our early work on IBVPs of dispersive equations \cite{li2020low,tao2001multilinear}.

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Cite

BibTeXRIS
BibTeX
@misc{xie2026initial,
  title = {{Initial and initial-boundary value problems for a cubic sixth-order Boussinesq equation}},
  author = {Yuhao Xie and Shenghao Li},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02748},
  eprint = {2610.02748},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02748},
}
RIS
TY  - UNPB
TI  - Initial and initial-boundary value problems for a cubic sixth-order Boussinesq equation
AU  - Yuhao Xie
AU  - Shenghao Li
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02748
UR  - https://arxiv.org/abs/2610.02748
AB  - In this paper, we consider the sixth-order Boussinesq equation with a cubic nonlinearity, u_tt−u_xx+k u_xxxx−u_xxxxxx+( u^3 ) _xx=0, with k=± 1, posed on both ℝ^+ and ℝ. The local wellposedness are improved in related Bourgain-type spaces, X^s,b, for s>−1/2 with b=1/2 and b>1/2 accordingly (See. \cite{esfahani2025well,zhong2024local}). The key ingredient is to refine the trilinear estimate on Burgain type space by adapting ideas from Tao's multiplier method, interpolation theory and our early work on IBVPs of dispersive equations \cite{li2020low,tao2001multilinear}.
ER  -