Navier-Stokes方程在涡-波数据下的全局时间无粘极限
Global-in-time inviscid limit of the Navier-Stokes equations for vortex-wave data
浏览论文内容
中文总结 AI 辅助
本文证明涡-波系统是二维Navier-Stokes方程在任意有限时间区间上的粘性消失极限，并给出两个分量的定量估计，实现全局时间合理性证明。
中文摘要 AI 辅助
我们证明了Marchioro和Pulvirenti在20世纪90年代引入的涡-波系统是二维Navier-Stokes方程在任意给定的有限时间区间上粘性消失极限。初始涡量由一个点涡和一个光滑、紧支撑且在涡附近消失的背景组成。正则分量强收敛到由涡-波系统控制的背景涡量，而集中分量则由以极限点涡轨迹为中心的Lamb-Oseen涡近似。我们获得了两个分量的定量估计，常数和粘性阈值依赖于所选时间区间，从而为此类初始数据提供了涡-波系统的全局时间合理性证明。
英文摘要
We justify the vortex-wave system introduced by Marchioro and Pulvirenti in the 1990s as the vanishing-viscosity limit of the two-dimensional Navier-Stokes equations on every prescribed finite time interval. The initial vorticity consists of a point vortex and a smooth, compactly supported background that vanishes near the vortex. The regular component converges strongly to the background vorticity governed by the vortex-wave system, while the concentrated component is approximated by a Lamb-Oseen vortex centered on the limiting point-vortex trajectory. We obtain quantitative estimates for both components, with constants and a viscosity threshold depending on the chosen time interval, thereby providing a global-in-time justification of the vortex-wave system for this class of initial data.
发表机构
- Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。
