Volume 11, Issue 2
The Stability of Navier-Stokes Equations and the Estimation of Its Attractor Dimension

Kaitai Li & Changbing Hu

J. Part. Diff. Eq., 11 (1998), pp. 125-136.

Published online: 1998-11

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  • Abstract
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].
  • Keywords

Navier-Stokes equations attractor unstability

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@Article{JPDE-11-125, author = {}, title = {The Stability of Navier-Stokes Equations and the Estimation of Its Attractor Dimension}, journal = {Journal of Partial Differential Equations}, year = {1998}, volume = {11}, number = {2}, pages = {125--136}, abstract = { 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].}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5559.html} }
TY - JOUR T1 - The Stability of Navier-Stokes Equations and the Estimation of Its Attractor Dimension 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].
Kaitai Li & Changbing Hu . (2019). The Stability of Navier-Stokes Equations and the Estimation of Its Attractor Dimension. Journal of Partial Differential Equations. 11 (2). 125-136. doi:
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