PreprintCC BY-NC-ND 4.0arXiv
On the effects of rotation on stationary Navier--Stokes equations in the half spaces in scale-critical spaces
Abstract
In this paper, we study the three-dimensional incompressible stationary Navier--Stokes equations with the Coriolis force in the half space with the inhomogeneous Dirichlet boundary condition. We show the existence of a unique small solution in the scale-critical Besov spaces. In particular, for any boundary data with only the normal component assumed to be sufficiently small, and for any external forces, we establish the well-posedness of the inhomogeneous Dirichlet boundary value problem when the speed of rotation is sufficiently large. In the proof, to exploit the stabilizing effect of the Coriolis term, we employ two explicit formulas depending on the relation between the horizontal frequency and the magnitude of the rotation speed.
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BibTeX
@misc{okazaki2026effects,
title = {{On the effects of rotation on stationary Navier--Stokes equations in the half spaces in scale-critical spaces}},
author = {Taiki Okazaki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25694},
eprint = {2610.25694},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25694},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - On the effects of rotation on stationary Navier--Stokes equations in the half spaces in scale-critical spaces
AU - Taiki Okazaki
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25694
UR - https://arxiv.org/abs/2610.25694
AB - In this paper, we study the three-dimensional incompressible stationary Navier--Stokes equations with the Coriolis force in the half space with the inhomogeneous Dirichlet boundary condition. We show the existence of a unique small solution in the scale-critical Besov spaces. In particular, for any boundary data with only the normal component assumed to be sufficiently small, and for any external forces, we establish the well-posedness of the inhomogeneous Dirichlet boundary value problem when the speed of rotation is sufficiently large. In the proof, to exploit the stabilizing effect of the Coriolis term, we employ two explicit formulas depending on the relation between the horizontal frequency and the magnitude of the rotation speed.
ER -