The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution

Chao Wang; Jingchao Yue; Zhifei Zhang

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arXiv · 2604.05765

The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution

Chao Wang·Jingchao Yue·Zhifei Zhang

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Abstract

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the existence and uniqueness of solutions subject to the non-slip boundary condition. This result was established in \cite{Ken} under the condition that the total mass is sufficiently small. Here, we eliminate the smallness assumption by analyzing the linearized operator near the point vortex and constructing a tailored functional framework-one designed to capture the distinct behaviors of the solution in the vicinity of the point vortex and the boundary, respectively.

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Chao Wang, Jingchao Yue, Zhifei Zhang. 2026-04-07. The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: construction of the solution. https://arxiv.org/abs/2604.05765

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