  For incompressible Navier-Stokes equations, Necas-Ruzicka-Sverak proved that
self-similar solution has to be zero in 1996. Further, Yang-Yang-Wu find
symmetry property plays an important role in the study of ill-posedness. In
this paper, we consider two types of symmetry property. We search special
symmetric and uniform analytic functions to approach the solution and establish
global uniform analytic and symmetric solution with initial value in general
symmetric Fourier-Herz space. For two kinds of symmetry of initial data, we
prove that the solution has also the same symmetric structure. Further, we
prove that the uniform analyticity is equivalent to the convolution inequality
on Herz spaces. By these ways, we can use symmetric and uniform analytic
functions to approximate the solution.
