On the stabilizing effects of rotation on stationary Navier--Stokes equations in the half spaces in scale-critical spaces
Year: 2026
Type: preprint
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 a vanishing normal component, 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.
Source: arXiv (Cornell University)
Author: Okazaki, Taiki
Institution: Tohoku University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: 回転を伴う非粘性流体方程式に対する解の安定性解析
OpenAlex ID: W7223028313