TY - JOUR
T1 - The Stability of Navier-Stokes Equations and the Estimation of Its Attractor Dimension
AU - Kaitai Li & Changbing Hu 
JO - Journal of Partial Differential Equations
VL - 2
SP - 125
EP - 136
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5559.html
KW - Navier-Stokes equations
KW - attractor
KW - unstability
AB -  In this paper, for a class of exterior force term 2s²W^'_{s,s} we analyse the existence of unstable modes of linearized Navier-Stokes Equations (NSE), and associate them with integer points in plane. Furthermore we give the lower boundary dimension estimation of the attractor of NSE. Liu discussed the condition where the exterior force term is W^'_{0,s} in (1, 2), but his method can't be extended to the condition where the exterior force term is W^'_{s_1,s_2} (s_1 ≠ 0, s_2 ≠ 0). So this paper may look as the extention of [1, 2]. The method which we give in this paper has direct application for further study of other properties of NSE (such as Hopf bifurcation). See [3].