On the energy spectrum for weak solutions of the Navier–Stokes equations
On the energy spectrum for weak solutions of the Navier–Stokes equations
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纳维-斯托克斯方程弱解的能谱
DOI：
10.1088/0951-7715/18/1/001
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
A. Mazzucato
中科院分区：
文献类型：
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作者：
A. Mazzucato
本文研究三维受迫Navier-Stokes方程弱解的能谱在高波数处的衰减。我们观察到，已知的正则性标准意味着解决方案是经常的，如果能量密度衰减在一个足够快的速度。这一结果也适用于一类具有无穷大整体能量的局部化Navier-Stokes方程的解。我们认为某些修改后的勒雷向后自相似的解决方案，这属于这一类，并表明，他们的能量谱衰减的临界速率的规律性。因此，这种衰减率与孤立的自相似奇点的出现是一致的。
We consider the decay at high wavenumbers of the energy spectrum for weak solutions to the three-dimensional forced Navier–Stokes equation in the whole space. We observe that known regularity criteria imply that solutions are regular if the energy density decays at a sufficiently fast rate. This result applies also to a class of solutions with infinite global energy by localizing the Navier–Stokes equation. We consider certain modified Leray backward self-similar solutions, which belong to this class, and show that their energy spectrum decays at the critical rate for regularity. Therefore, this rate of decay is consistent with the appearance of an isolated self-similar singularity.