Rigidity of Landau solution in the rotated self-similar class
Abstract
Landau solution is a special family of solutions to the stationary Navier Stokes equations, which is important for the study of stationary problems such as asymptotic behavior and regularity. In this paper we prove that the Landau solution is rigid in rotated self-similar class when rotation parameter α sufficiently small or large. The arguments in the two parts rely on different approaches. For small rotation, we use the compactness argument and establish a classification lemma of the self-similar kernel of the linearization around any Landau solution, this method can also be extended to DSS and RDSS cases. For large rotation, the strong angular dissipation produces additional coercivity on the non-axisymmetric component, which forces the solution to reduce into Landau solution.
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BibTeX
@misc{shi2026rigidity,
title = {{Rigidity of Landau solution in the rotated self-similar class}},
author = {Yuxuan Shi and Liqun Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24261},
eprint = {2609.24261},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24261},
}
RIS
TY - UNPB
TI - Rigidity of Landau solution in the rotated self-similar class
AU - Yuxuan Shi
AU - Liqun Zhang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24261
UR - https://arxiv.org/abs/2609.24261
AB - Landau solution is a special family of solutions to the stationary Navier Stokes equations, which is important for the study of stationary problems such as asymptotic behavior and regularity. In this paper we prove that the Landau solution is rigid in rotated self-similar class when rotation parameter α sufficiently small or large. The arguments in the two parts rely on different approaches. For small rotation, we use the compactness argument and establish a classification lemma of the self-similar kernel of the linearization around any Landau solution, this method can also be extended to DSS and RDSS cases. For large rotation, the strong angular dissipation produces additional coercivity on the non-axisymmetric component, which forces the solution to reduce into Landau solution.
ER -