\`x^2+y_1+z_12^34\`
Advanced Search
Advanced Search
Advanced Search
This issue Previous Article Next Article
Article Contents
Article Contents
2010, Volume 26, Issue 3: 781-794. Doi: 10.3934/dcds.2010.26.781
This issue Previous Article Next Article Support of maximizing measures for typical $\mathcal{C}^0$ dynamics on compact manifolds

An inviscid dyadic model of turbulence: The global attractor

  • 1.

    Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 60607-7045

  • 2.

    Department of Mathematics, University of Southern California, 3620 South Vermont Ave., KAP 108, Los Angeles, CA 90089

  • 3.

    Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, Texas 78712

Received:  July 31, 2008
Revised:  October 31, 2009
Published:  August 2010
Abstract Related Papers Cited by
    Abstract
  • Properties of an infinite system of nonlinearly coupled ordinary differential equations are discussed. This system models some properties present in the equations of motion for an inviscid fluid such as the skew symmetry and the 3-dimensional scaling of the quadratic nonlinearity. In a companion paper [8] it is proved that every solution for the system with forcing blows up in finite time in the Sobolev $H^{5/6}$ norm. In this present paper, it is proved that after the blow-up time all solutions stay in $H^s$, $s < 5/6$ for almost all time. It is proved that the model system exhibits the phenomenon of anomalous (or turbulent) dissipation which was conjectured for the Euler equations by Onsager. As a consequence of this anomalous dissipation the unique equilibrium of the system is a global attractor.
    Mathematics Subject Classification: Primary: 35Q31; Secondary: 37L30.

    Citation:
    shu

    \begin{equation} \\ \end{equation}
    • Related Papers
  • Cited by
  • Access History
  • 加载中
PDF
XML
Export Citation
SHARE
Email to a Friend

Article Metrics

HTML views() PDF downloads(134) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return
    Site map Copyright © 2023 American Institute of Mathematical Sciences