A Helmholtz-type decomposition for the space of symmetric matrices
A Helmholtz-type decomposition for the space of symmetric matrices
复制标题
对称矩阵空间的亥姆霍兹型分解
DOI：
10.1090/btran/167
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
E. Sawyer
中科院分区：
文献类型：
--
作者：
E. Miller;E. Sawyer
在本文中，我们引入了平方可积对称矩阵值函数空间的亥姆霍兹型分解，类似于矢量场的标准亥姆霍兹分解。这种分解可以更好地理解应变约束空间，这对于纳维-斯托克斯正则问题很重要。特别是，我们给出了应变约束空间的正交补的完整表征，并研究了应变约束空间中矩阵特征值分布的几何形状。
In this paper, we introduce a Helmholtz-type decomposition for the space of square integrable, symmetric-matrix-valued functions analogous to the standard Helmholtz decomposition for vector fields. This decomposition provides a better understanding of the strain constraint space, which is important to the Navier–Stokes regularity problem. In particular, we give a full characterization the orthogonal complement of the strain constraint space and investigate the geometry of the eigenvalue distribution of matrices in the strain constraint space.