The Uniqueness of Nondecaying Solutions for the Navier-Stokes Equations
The Uniqueness of Nondecaying Solutions for the Navier-Stokes Equations
复制标题
纳维-斯托克斯方程非衰变解的唯一性
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
J. Kato
中科院分区：
文献类型：
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作者：
J. Kato
摘要：当速度场有界且压力场是有界初始数据的 BMO 值局部时间可积函数时，纳维-斯托克斯方程在整个空间中解的唯一性成立。这里速度场可能不会在无限远的空间衰减。尽管在没有衰减假设的情况下有一些关于唯一性的结果，但我们的结果是新的并且适用于通过求解积分方程构造的解。
Abstract.The uniqueness of solutions of the Navier-Stokes equations in the whole space is established when the velocity field is bounded and the pressure field is a BMO-valued locally integrable-in-time function for bounded initial data. Here the velocity field may not decay at space infinity. Although there are a few results concerning uniqueness without the decay assumption, our result is new and applicable for solutions constructed by solving the integral equations.