Two-dimensional incompressible viscous flow around a small obstacle
Two-dimensional incompressible viscous flow around a small obstacle
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小障碍物周围的二维不可压缩粘性流
DOI：
10.1007/s00208-006-0012-z
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发表时间：
2003
影响因子：
1.4
通讯作者：
H. N. Lopes
中科院分区：
文献类型：
--
作者：
D. Iftimie;M. L. Filho;H. N. Lopes
本文研究了二维粘性不可压缩流动在小物质障碍物外的渐近行为。我们固定了绕障碍物的初始涡量ω 0和环量γ。证明了当γ足够小时，极限流满足全平面Navier-Stokes方程组，初始涡量为ω0+ γδ，其中δ为标准Dirac测度.该结果应与作者在Iftimie等人中得到的相应的无粘结果进行对比。（Comm. Part.不一样Eqn.28，349-379（2003）），其中小障碍物的影响出现在PDE的系数中，而不仅仅出现在初始数据中。证明的主要内容是外区域中Stokes算子的Lp − Lq估计，加藤不动点方法的先验估计，能量估计，重正化和插值。
In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω0and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier–Stokes system, with initial vorticity ω0+ γδ, where δ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in Iftimie et al. (Comm. Part. Differ. Eqn.28, 349–379 (2003)), where the effect of the small obstacle appears in the coefficients of the PDE and not only in the initial data. The main ingredients of the proof areLp−Lqestimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato’s fixed point method, energy estimates, renormalization and interpolation.