On Vorticity Directions near Singularities for the Navier-Stokes Flows with Infinite Energy
On Vorticity Directions near Singularities for the Navier-Stokes Flows with Infinite Energy
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DOI：
10.1007/s00220-011-1197-x
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发表时间：
2010-04
影响因子：
2.4
通讯作者：
Y. Giga;H. Miura
中科院分区：
文献类型：
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作者：
Y. Giga;H. Miura
对于初值有界且具有无穷大能量的三维Navier-Stokes流，给出了涡量方向的几何非爆破准则。我们证明了在时间行为的限制下（I型条件）的解决方案不爆破，如果涡度方向是一致连续的涡度大小是大的地方。这改进了P. Constantin和C. 1993年，Fergusman提出了有限能量弱解。我们的方法是基于一个简单的爆破参数，即在涡度方向连续的情况下，情况看起来像二维的。我们还讨论了边值问题。
We give a geometric nonblow-up criterion on the direction of the vorticity for the three dimensional Navier-Stokes flow whose initial data is just bounded and may have infinite energy. We prove that under a restriction on behavior in time (type I condition) the solution does not blow up if the vorticity direction is uniformly continuous at the place where the vorticity magnitude is large. This improves the regularity condition for the vorticity direction first introduced by P. Constantin and C. Fefferman (1993) for finite energy weak solution. Our method is based on a simple blow-up argument which says that the situation looks like two-dimensional under continuity of the vorticity direction. We also discuss boundary value problems.