The navier-stokes flow with linearly growing initial velocity in the whole space
The navier-stokes flow with linearly growing initial velocity in the whole space
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全空间初速度线性增长的纳维-斯托克斯流
DOI：
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发表时间：
2009
期刊：
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通讯作者：
O. Sawada
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文献类型：
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作者：
O. Sawada
本文构造了Navier-Stokes方程在整个空间中，当速度在无穷远处线性增长时解的唯一性。对于某个常数矩阵M和某个函数u，速度可以选择为Mx + u(x)。摄动u取在一些齐次Besov空间中，这些空间在空间无穷处包含一些非衰减函数，通常是一些概周期函数。同时也证明了当M本质上是偏对称的时，在二维或三维空间中存在一个局部时间解。
In this paper, the uniqueness of the solutions to the Navier-Stokes equations in the whole space is constructed, provided that the velocity grows linearly at infinity. The velocity can be chosen as Mx + u(x) for some constant matrix M and some function u. The perturbation u is taken in some homogeneous Besov spaces, which contain some nondecaying functions at space infinity, typically, some almost periodic functions. It is also proved that a locally-in-time solution exists, when M is essentially skew-symmetric which demonstrates the rotating fluid in 2- or 3-dimension.