arXiv subjects

Jingchao Yue

Publications and source records attributed to Jingchao Yue.

3 recordsLinked to original sources

arXiv2026

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

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.

math.AP↗

arXiv2026

The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: Zero-viscosity limit

This is the second of two papers devoted to the asymptotic behavior of solutions to the incompressible Navier-Stokes equations in a half-space with point vortex initial data. A major difficulty stems from the interaction between the point vortex initial data and the boundary, which complicates the derivation of a valid asymptotic expansion. To overcome this, we carry out a precise matching between the point vortex and boundary-layer profiles to accurately capture the correct viscous behavior of the vortex in the half-plane. Based on this matched asymptotic analysis, we decompose the vorticity into three components: vorticity near the point vortex, vorticity near the boundary, and vorticity in the transition layer. A key point is that each component must be analyzed in its own distinct region. On this basis, we establish refined estimates and thereby achieve the inviscid limit for the point vortex. Finally, we rigorously prove that solutions to the Navier-Stokes equations converge to the Lamb-Oseen vortex away from the boundary, while approaching the Prandtl boundary-layer system in the near-boundary region.

math.AP↗

arXiv2025

The interaction between rough vortex patch and boundary layer

In this paper, we investigate the asymptotic behavior of solutions to the Navier-Stokes equations in the half-plane under high Reynolds number conditions, where the initial vorticity belongs to the Yudovich class and is supported away from the boundary. We establish the $L^p$ ($2\leq p< \infty$) convergence of solutions from the Navier-Stokes equations to those of the Euler equations. One of the main difficulties stems from the limited regularity of the initial data, which hinders the derivation of an asymptotic expansion. To overcome this challenge, we first prove a Kato-type criterion adapted to the Yudovich class setting. We then obtain uniform estimates for the Navier-Stokes equations -- a non-trivial task due to the strong boundary layer effects. A key component of our approach is the introduction of a suitable functional framework, which enables us to control the interaction between the rough vortex patch and the boundary layer.

math.AP↗