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Validity of three-dimensional axisymmetric steady Prandtl expansion
Abstract
We study steady axisymmetric Navier--Stokes flows with swirl in the circular cylinder 𝒞L=(0,L)× B2(0,1) with the no-slip condition on the stationary lateral wall. For the leading Euler velocity (ue0,we0,θe0)=(1,0,r K(r)), where K(r)=H(r2) is a prescribed smooth radial function, we construct and justify a Prandtl expansion as ε → 0 for sufficiently small fixed L. The expansion accounts for both axial and azimuthal boundary layers, including the case of a Blasius leading axial profile with nonzero swirl. Weighted estimates at the symmetry axis and coupled remainder estimates yield a uniform velocity error bound.
Related
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BibTeX
@misc{guo2026validity,
title = {{Validity of three-dimensional axisymmetric steady Prandtl expansion}},
author = {Yan Guo and Hailiang Li and Xiangyu Ma and Mingyue Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02492},
eprint = {2611.02492},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02492},
}
RIS
TY - UNPB
TI - Validity of three-dimensional axisymmetric steady Prandtl expansion
AU - Yan Guo
AU - Hailiang Li
AU - Xiangyu Ma
AU - Mingyue Zhang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.02492
UR - https://arxiv.org/abs/2611.02492
AB - We study steady axisymmetric Navier--Stokes flows with swirl in the circular cylinder 𝒞_L=(0,L)× B_2(0,1) with the no-slip condition on the stationary lateral wall. For the leading Euler velocity (u_e^0,w_e^0,θ_e^0)=(1,0,r K(r)), where K(r)=H(r^2) is a prescribed smooth radial function, we construct and justify a Prandtl expansion as ε → 0 for sufficiently small fixed L. The expansion accounts for both axial and azimuthal boundary layers, including the case of a Blasius leading axial profile with nonzero swirl. Weighted estimates at the symmetry axis and coupled remainder estimates yield a uniform velocity error bound.
ER -