A remark on the uniqueness of Kozono-Nakao’s mild L^3-solutions on the whole time axis to the Navier-Stokes equations in unbounded domains
A remark on the uniqueness of Kozono-Nakao’s mild L^3-solutions on the whole time axis to the Navier-Stokes equations in unbounded domains
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论Kozono-Nakao全时间轴上的温和L^3-解对无界域纳维-斯托克斯方程的唯一性
DOI：
10.1007/s42985-021-00121-8
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Taniuchi Yasushi
中科院分区：
文献类型：
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作者：
Taniuchi Yasushi
本文讨论了三维无界区域上Navier-Stokes方程的Kozono-Nakao有界连续解在整个时间轴上的唯一性。当是一个无界区域时，已知小解在具有充分小范数的解类中是唯一的。还有另一种类型的唯一性定理。Farwig，Nakatsuka和作者（2015）表明，如果对于相同的力存在两个解，其中一个很小，并且如果另一个满足预紧范围条件（PRC），则两个解重合。由于时间周期解满足（PRC），所以这个唯一性定理也适用于时间周期解。另一方面，存在许多不满足（PRC）的解。在本文中，通过假设一些-范数的有界性，我们得到了上述唯一性定理的一个修正版本，没有（PRC）。
This paper is concerned with the uniqueness of Kozono–Nakao’s bounded continuous-solutions on the whole time axis to the Navier–Stokes equations in 3-dimensional unbounded domains. Whenis an unbounded domain, it is known that a small solution inis unique within the class of solutions which have sufficiently small-norm. There is another type of uniqueness theorem. Farwig, Nakatsuka and the author (2015) showed that if two solutions exist for the same forcef, one is small and if other one satisfies the precompact range condition (PRC), then the two solutions coincide. Since time-periodic solutions satisfy (PRC), this uniqueness theorem is applicable to time-periodic solutions. On the other hand, there exist many solutions which do not satisfy (PRC). In this paper, by assuming the boundedness of the-norm for some, we show a modified version of the above-mentioned uniqueness theorem without (PRC).