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uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab

  • Han Li
  • Jingwen Han
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Abstract

In this paper, we investigate the uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab domain with no-slip boundary conditions. Specifically, under the given external force and the small Poiseuille flow assumptions, we prove that there is an H1 solution, and obtain the pointwise decay around the Poiseuille flow at far field. Furthermore, if the force is small, the solution is shown to be unique. The key point of the proof is the estimate of the Dirichlet integral of the solutions in the truncated domains and the Stokes regularity estimates.

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Cite

BibTeXRIS
BibTeX
@misc{li2026uniqueness,
  title = {{uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab}},
  author = {Han Li and Jingwen Han},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29138},
  eprint = {2608.29138},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29138},
}
RIS
TY  - UNPB
TI  - uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab
AU  - Han Li
AU  - Jingwen Han
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29138
UR  - https://arxiv.org/abs/2608.29138
AB  - In this paper, we investigate the uniqueness and asymptotic behavior of the stationary Navier-Stokes equations in a slab domain with no-slip boundary conditions. Specifically, under the given external force and the small Poiseuille flow assumptions, we prove that there is an H1 solution, and obtain the pointwise decay around the Poiseuille flow at far field. Furthermore, if the force is small, the solution is shown to be unique. The key point of the proof is the estimate of the Dirichlet integral of the solutions in the truncated domains and the Stokes regularity estimates.
ER  -