TY - JOUR T1 - On the Lorenz Systems for the Incompressible Flow Between Two Concentric Rotating Cylinders JO - Journal of Partial Differential Equations VL - 3 SP - 209 EP - 221 PY - 2010 DA - 2010/08 SN - 23 DO - http://doi.org/10.4208/jpde.v23.n3.1 UR - https://global-sci.org/intro/article_detail/jpde/5230.html KW - Couette-Taylor flow KW - attractor KW - Hausdorff dimension AB -

A spectral method is used to derive a series of equations for axisymmetric Couette-Taylor flow. A three-modes system, which is similar to the Lorenz systems, is obtained by a suitable three-modes truncation of the Navier-Stokes equations for the incompressible flow between two concentric rotating cylinders. The stability of the three-modes systems is discussed. Moreover, the existence of its attractor and the estimation of Hausdorff dimension are given.