Nonstationary navier-stokes flows in a two-dimensional exterior domain with rotational symmetries
Nonstationary navier-stokes flows in a two-dimensional exterior domain with rotational symmetries
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DOI：
10.1512/iumj.2006.55.2726
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发表时间：
2006
影响因子：
1.1
通讯作者：
Cheng He;Tetsuro Miyakawa
中科院分区：
文献类型：
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作者：
Cheng He;Tetsuro Miyakawa
在二维外部区域中，我们寻找与边界相关的总净力为零的Navier-Stokes流（见（1.2））。结果表明，这是在每一个时间的情况下，只要初速度是可加的，并具有一定的规律性和旋转对称性。结果表明，这种可和性、正则性和旋转对称性的条件在时间上是保持的。一个渐近的配置文件推导出的时间衰减率的下限估计发现这样的解决方案。此外，存在的流动具有较高的对称性，其时间衰减率超过上述下限。衰变率与对称群的阶数直接相关。
In a 2D exterior domain, we look for Navier-Stokes flows for which the associated total net force to the boundary vanishes (see (1.2)). It is shown that this is the case at each time whenever the initial velocity is summable and possesses some regularity and rotational symmetry. The result shows that this condition of summability, regularity and rotational symmetry is preserved in time. An asymptotic profile is deduced and a lower bound estimate on time-decay rates is found for such solutions. Moreover, existence is shown for flows with higher symmetry for which the time-decay rates exceed the above-mentioned lower bound. The decay rates are directly connected with the orders of groups of symmetry.