Global regularity for some classes of large solutions to the Navier-Stokes equations
Global regularity for some classes of large solutions to the Navier-Stokes equations
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DOI：
10.4007/annals.2011.173.2.9
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发表时间：
2008-07
影响因子：
4.9
通讯作者：
J. Chemin;I. Gallagher;M. Paicu
中科院分区：
文献类型：
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作者：
J. Chemin;I. Gallagher;M. Paicu
在前两位作者以前的工作中，提出了三维不可压缩Navier-Stokes方程的初始数据类，虽然初始数据的范数可以任意大，但可以产生全局光滑解。其中一项研究所考虑的初始数据的主要特点是，它在一个方向上变化缓慢，尽管在某种意义上它是“准备充分的”（其标准很大，但不取决于慢参数）。本文的目的是将这种设置推广到一种“准备不足”的情况（当小参数趋于零时，规范就会崩溃）。与这些作品一样，证明使用了方程非线性项的特殊结构。
In previous works by the first two authors, classes of initial data to the three-dimensional, incompressible Navier-Stokes equations were presented, generating a global smooth solution although the norm of the initial data may be chosen arbitrarily large. The main feature of the initial data considered in one of those studies is that it varies slowly in one direction, though in some sense it is "well-prepared" (its norm is large but does not depend on the slow parameter). The aim of this article is to generalize that setting to an "ill prepared" situation (the norm blows up as the small parameter goes to zero). As in those works, the proof uses the special structure of the nonlinear term of the equation.