On the zero-viscosity limit of the Navier–Stokes equations in R+3 without analyticity
On the zero-viscosity limit of the Navier–Stokes equations in R+3 without analyticity
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DOI：
10.1016/j.matpur.2017.09.007
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发表时间：
2017-09
期刊：
影响因子：
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通讯作者：
Mingwen Fei;T. Tao;Zhifei Zhang
中科院分区：
文献类型：
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作者：
Mingwen Fei;T. Tao;Zhifei Zhang
本文研究了R+ 3中具有非滑移边界条件的不可压Navier-Stokes方程的零粘性极限，其中初始涡量远离边界。与2-D情况不同，这种数据在（x，y）中不是解析的，因为y靠近3-D中的边界。Maekawa证明了R+ 2中的Navier-Stokes方程在时间上局部收敛于边界层外的Euler方程和边界层内的Prandtl方程。他的证明使用了柯西-科瓦莱斯卡亚定理，其中涡度公式和欧拉-普朗特分解起着重要作用。本文利用直接能量方法将Maekawa的结果推广到R+ 3，使其适用于一般的物理区域。
We consider the zero viscosity limit of the incompressible Navier–Stokes equations with non-slip boundary condition in R+ 3 for the initial vorticity located away from the boundary. Unlike 2-D case, this kind of data is not analytic in (x, y) for y close to the boundary in 3-D. Maekawa proved the local in time convergence of the Navier–Stokes equations in R+ 2 to the Euler equations outside a boundary layer and to the Prandtl equations in the boundary layer. His proof used Cauchy–Kowaleskaya theorem, where the vorticity formulation and Euler–Prandtl decomposition play an important role. In this paper, we generalize Maekawa's result to R+ 3 by using a direct energy method, which may be applicable for general physical domain.