Remark on the Rate of Decay of Higher Order Derivatives for Solutions to the Navier–Stokes Equations in Rn☆
Remark on the Rate of Decay of Higher Order Derivatives for Solutions to the Navier–Stokes Equations in Rn☆
复制标题
DOI：
10.1006/jfan.1999.3550
复制
发表时间：
2000-04
影响因子：
1.7
通讯作者：
M. Oliver;E. Titi
中科院分区：
文献类型：
--
作者：
M. Oliver;E. Titi
给出了Rn中非受迫Navier-Stokes方程解的高阶导数衰减的一个新的上界的推导。该方法基于所谓的Gevrey估计，还给出了解的解析半径在时间上增长的显式界。此外，在假设Navier-Stokes解在L2范数下保持足够接近热方程解的情况下--已知这一结果对于一大类初始数据是正确的--可以得到高阶导数衰减的下界。
We present a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier–Stokes equations in Rn. The method, based on so-called Gevrey estimates, also yields explicit bounds on the growth of the radius of analyticity of the solution in time. Moreover, under the assumption that the Navier–Stokes solution stays sufficiently close to a solution of the heat equation in the L2 norm—a result known to be true for a large class of initial data—lower bounds on the decay of higher order derivatives can be obtained.