Gevrey regularity of solutions to the 3-D Navier-Stokes equations with weighted $l_p$ initial data
Gevrey regularity of solutions to the 3-D Navier-Stokes equations with weighted $l_p$ initial data
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DOI：
10.1512/iumj.2007.56.2891
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发表时间：
2007
影响因子：
1.1
通讯作者：
A. Biswas;David Swanson
中科院分区：
文献类型：
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作者：
A. Biswas;David Swanson
当初值的Fourier系数序列位于适当的加权lp空间时，证明了三维周期Navier-Stokes方程局部解的存在性和Gevrey正则性.我们的工作受到Foias和Temam（[10]）的启发，得到了他们结果的推广.特别是，我们的分析允许初始数据比[10]中更不平滑，并且也可以具有无限大的能量。我们的主要工具是一个变种的杨卷积不等式，使我们能够估计加权LP范数的非线性项。
We prove the existence and Gevrey regularity of local solutions of the three dimensional periodic Navier-Stokes equations in case the sequence of Fourier coefficients of the initial data lies in an appropriate weighted lp space. Our work is motivated by that of Foias and Temam ([10]) and we obtain a generalization of their result. In particular, our analysis allows for initial data that are less smooth than in [10] and can also have infinite energy. Our main tool is a variant of the Young convolution inequality enabling us to estimate the nonlinear term in weighted lp norm.