4.6 Article

One-Dimensional Parametric Determining form for the Two-Dimensional Navier-Stokes Equations

期刊

JOURNAL OF NONLINEAR SCIENCE
卷 27, 期 5, 页码 1513-1529

出版社

SPRINGER
DOI: 10.1007/s00332-017-9375-4

关键词

Navier-Stokes equations; Global attractors; Determining nodes; Determining form; Parametric determining form; Determining parameter

资金

  1. National Science Foundation (NSF) [DMS-1109784]
  2. Office of Naval Research (ONR) [N00014-15-1-2333]
  3. NSF [DMS-1418911, DMS-1109640, DMS-1109645]
  4. Leverhulme Trust [VP1-2015-036]
  5. ONR [N00014-15-1-2333]
  6. Division Of Mathematical Sciences
  7. Direct For Mathematical & Physical Scien [1418911] Funding Source: National Science Foundation

向作者/读者索取更多资源

The evolution of a determining form for the 2D Navier-Stokes equations (NSE) which is an ODE on a space of trajectories is completely described. It is proved that at every stage of its evolution, the solution is a convex combination of the initial trajectory and a chosen, fixed steady state, with a dynamical convexity parameter theta, which will be called the characteristic determining parameter. That is, we show a separation of variables formula for the solution of the determining form. Moreover, for a given initial trajectory, the dynamics of the infinite-dimensional determining form are equivalent to those of the characteristic determining parameter theta which is governed by a one-dimensional ODE. This one-dimensional ODE is used to show that if the solution to the determining form converges to the fixed state it does so no faster than O(tau(-1/2)) , otherwise it converges to a projection of some other trajectory in the global attractor of the NSE, but no faster than O(tau(-1)) , as tau -> infinity, where tau is the evolutionary variable in determining form. The one-dimensional ODE is also exploited in computations which suggest that the one-sided convergence rate estimates are in fact achieved. The ODE is then modified to accelerate the convergence to an exponential rate. It is shown that the zeros of the scalar function that governs the dynamics of theta, which are called characteristic determining values, identify in a unique fashion the trajectories in the global attractor of the 2D NSE.

作者

我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。

评论

主要评分

4.6
评分不足

次要评分

新颖性
-
重要性
-
科学严谨性
-
评价这篇论文

推荐

暂无数据
暂无数据