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arXiv 0807.1265math.AP
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Navier-斯托克斯方程几类大解的整体正则性

Global regularity for some classes of large solutions to the Navier-Stokes equations

Jean-Yves Chemin, Isabelle Gallagher, Marius Paicu

摘要:

在两个第一作者的前三篇论文中,提出了三维不可压缩Navier-斯托克斯方程的初始数据类,尽管初始数据的范数可以选择任意大,但产生了全局光滑解。在上一篇论文中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“良好的”(它的范数很大,但不依赖于慢参数)。本文的目的是将上一篇文章的设置推广到"病态“的情况(当小参数趋于零时范数爆炸)。证明使用了方程的非线性项的特殊结构。

英文摘要:

In three previous papers by the two first 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 the last paper 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 the setting of that last paper to an ``ill prepared'' situation (the norm blows up as the small parameter goes to zero).The proof uses the special structure of the nonlinear term of the equation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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