Self-similar stationary Navier--Stokes flows in a half-space with arbitrarily large swirl forcing
Abstract
We study axisymmetric self-similar solutions of the stationary Navier--Stokes equations with (−3)-homogeneous forces and no-slip boundary conditions in a half-space. For a fixed force without swirl, we characterize the interval of amplitudes for which solutions exist and describe the velocity singularity at its finite endpoints. For each parameter in this interval, a solution exists after adding a swirl force of any size, and it is unique among solutions with bounded profiles when the swirl force is sufficiently small. The proof uses the nonnegative contribution of swirl to a Riccati equation and a comparison estimate. We also prove that, when the tangential curl of the force is sufficiently small, there exists a unique solution with small velocity profiles.
Related
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BibTeX
@misc{wang2026selfsimilar,
title = {{Self-similar stationary Navier--Stokes flows in a half-space with arbitrarily large swirl forcing}},
author = {Yun Wang and Chunjing Xie and Shaoheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.25432},
eprint = {2608.25432},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25432},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Self-similar stationary Navier--Stokes flows in a half-space with arbitrarily large swirl forcing
AU - Yun Wang
AU - Chunjing Xie
AU - Shaoheng Zhang
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2608.25432
UR - https://arxiv.org/abs/2608.25432
AB - We study axisymmetric self-similar solutions of the stationary Navier--Stokes equations with (−3)-homogeneous forces and no-slip boundary conditions in a half-space. For a fixed force without swirl, we characterize the interval of amplitudes for which solutions exist and describe the velocity singularity at its finite endpoints. For each parameter in this interval, a solution exists after adding a swirl force of any size, and it is unique among solutions with bounded profiles when the swirl force is sufficiently small. The proof uses the nonnegative contribution of swirl to a Riccati equation and a comparison estimate. We also prove that, when the tangential curl of the force is sufficiently small, there exists a unique solution with small velocity profiles.
ER -