Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
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DOI：
10.1090/s0002-9947-10-04744-6
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发表时间：
2007-10
影响因子：
1.3
通讯作者：
J. Chemin;I. Gallagher
中科院分区：
文献类型：
--
作者：
J. Chemin;I. Gallagher
在作者以前的论文中，提出了三维不可压缩Navier-Stokes方程的初始数据类，尽管初始数据的范数可以任意选择，但可以产生全局光滑解。本文的目的是提供新的例子，任意大的初始数据产生的全球解决方案，在整个空间。与前面的例子相反，初始数据没有特定的振荡特性，而是在一个方向上缓慢变化。证明利用了方程非线性项的特殊结构。
In to previous papers by the 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 aim of this article is to provide new examples of arbitrarily large initial data giving rise to global solutions, in the whole space. Contrary to the previous examples, the initial data has no particular oscillatory properties, but varies slowly in one direction. The proof uses the special structure of the nonlinear term of the equation.