On the maximal space analyticity radius for the 3D Navier–Stokes equations and energy cascades
On the maximal space analyticity radius for the 3D Navier–Stokes equations and energy cascades
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关于 3D 纳维-斯托克斯方程和能量级联的最大空间解析半径
DOI：
10.1007/s10231-012-0300-z
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发表时间：
2014
影响因子：
1
通讯作者：
C. Foias
中科院分区：
文献类型：
--
作者：
A. Biswas;C. Foias
本文研究了Navier-Stokes方程正则解的最大空间解析半径及其与湍流的关系。为了做到这一点，我们引入了一个新的辅助常微分方程的解析半径的演变涉及Gevrey类规范。我们进一步证明了在最大空间解析性半径上的跳跃是一个间歇性事件，并且与逆能量级联有关。我们的方法也导致了一种新的类型的全球性的Navier-Stokes方程的正则性测试。
In this paper, we study the maximal space analyticity radius associated with a regular solution of the Navier–Stokes equations and its connection to turbulence. In order to do this, we introduce a new auxiliary ODE for the evolution of the analyticity radius involving the Gevrey class norms. We further show that jumps in the maximal space analyticity radius are an intermittent event and are connected to inverse energy cascade. Our approach also leads to a new type of global regularity test for the Navier–Stokes equation.