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Stabilization of hydroelastic waves in deep water

  • Jian Li
  • Shaojie Yang
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Abstract

We consider the stabilization of two-dimensional periodic hydroelastic waves in deep water beneath a massless nonlinear Cosserat sheet by means of a localized pres- sure feedback. For sufficiently regular solutions, under an explicit condition relating gravity, flexural rigidity and the localization profile, we prove a uniform spacetime estimate and a localized dissipation observability inequality. As a consequence, the hydroelastic Hamiltonian decays quantitatively as long as the solution remains in a small geometric regime. The proof combines an energy dissipation identity with a nonlinear multiplier method adapted to the infinite-depth geometry, together with a coercivity analysis of the Cosserat bending energy.

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Cite

BibTeXRIS
BibTeX
@misc{li2026stabilization,
  title = {{Stabilization of hydroelastic waves in deep water}},
  author = {Jian Li and Shaojie Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21769},
  eprint = {2609.21769},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21769},
}
RIS
TY  - UNPB
TI  - Stabilization of hydroelastic waves in deep water
AU  - Jian Li
AU  - Shaojie Yang
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21769
UR  - https://arxiv.org/abs/2609.21769
AB  - We consider the stabilization of two-dimensional periodic hydroelastic waves in deep water beneath a massless nonlinear Cosserat sheet by means of a localized pres- sure feedback. For sufficiently regular solutions, under an explicit condition relating gravity, flexural rigidity and the localization profile, we prove a uniform spacetime estimate and a localized dissipation observability inequality. As a consequence, the hydroelastic Hamiltonian decays quantitatively as long as the solution remains in a small geometric regime. The proof combines an energy dissipation identity with a nonlinear multiplier method adapted to the infinite-depth geometry, together with a coercivity analysis of the Cosserat bending energy.
ER  -