The resolution of the Navier-Stokes equations in anisotropic spaces
The resolution of the Navier-Stokes equations in anisotropic spaces
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DOI：
10.4171/rmi/248
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发表时间：
1999-04
影响因子：
1.2
通讯作者：
D. Iftimie
中科院分区：
文献类型：
--
作者：
D. Iftimie
本文证明了具有小初始数据的三维Navier-Stokes方程在第i个方向为Hdi， d1 + d2 + d3 = 1/2, -1/2 < di < 1/2，前两个方向为L2，第三个方向为B2,11/2，其中H和B表示通常的齐次Sobolev和Besov空间中解的整体存在唯一性。
In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are Hdi in the i-th direction, d1 + d2 + d3 = 1/2, -1/2 < di < 1/2 and in a space which is L2 in the first two directions and B2,11/2 in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.