Global Axisymmetric Solutions to Three-Dimensional Navier–Stokes System
Global Axisymmetric Solutions to Three-Dimensional Navier–Stokes System
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DOI：
10.1093/imrn/rns232
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发表时间：
2014
影响因子：
1
通讯作者：
Ping Zhang;Ting Zhang
中科院分区：
文献类型：
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作者：
Ping Zhang;Ting Zhang
本文研究了具有轴对称初始数据的三维Navier-Stokes系统的全局适定性，并考虑了初始速度场的旋流分量的各种小条件。特别地，我们证明了对于足够大的M，如果足够小（相对于∥u0∥L2，，和），则（1.1）有一个唯一的全局光滑解。进一步证明了在有限时间内，只要局部轴对称光滑解u满足δ>,β bbb6，或(α,β)=(4,6)，且yu不爆破。
In this paper, we investigate the global well-posedness of three-dimensional Navier–Stokes system with the axisymmetric initial data and with various types of smallness conditions on the swirl componentof the initial velocity field. In particular, we proved that ifis sufficiently small (compared with ∥u0∥L2,, and) for M large enough, then (1.1) has a unique global smooth solution. Furthermore, we prove that as long as the local axisymmetric smooth solution u satisfyingfor δ>0,β>6, or (α,β)=(4,6), and anyu will not blow-up in finite time.