The Inviscid Limit of Navier--Stokes Equations for Vortex-Wave Data on $\mathbb R^2$
The Inviscid Limit of Navier--Stokes Equations for Vortex-Wave Data on $\mathbb R^2$
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纳维无粘极限--$mathbb R^2$ 上涡波数据的斯托克斯方程
DOI：
10.1137/19m1246602
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发表时间：
2019
影响因子：
2
通讯作者：
Nguyen, Trinh T.
中科院分区：
文献类型：
--
作者：
Nguyen, Toan T.;Nguyen, Trinh T.
对于涡度为点涡和规则分量叠加的初始数据，我们建立了不可压N-S方程在全平面上的无粘性极限。特别是，这严格地证明了涡波系统与消失粘性极限中的物理Navier-Stokes流动的合理性，该模型由Marchioro和Pulvirenti在90年代初提出，用于描述规则环境涡度背景下的点涡动力学。这一证明是基于盖雷在推导涡点系统时所作的分析而得出的。
We establish the inviscid limit of the incompressible Navier--Stokes equations on the whole planefor initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier--Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.