# American Institute of Mathematical Sciences

February  2004, 10(1&2): 253-268. doi: 10.3934/dcds.2004.10.253

## Recurrence in the 2-$D$ Navier--Stokes equations

 1 Department of Mathematics, Texas A&M University, College Station, TX 77843, United States, United States 2 Department of Mathematics, Indiana University, Bloomington, IN, 47405, United States

Received  January 2003 Revised  July 2003 Published  October 2003

Part of the Kolmogorov-Kraichnan-Batchelor theory of turbulence concerns the average enstrophy flux across wave numbers. To support that theory, rigorous relations involving both the net and one-way flux are established using ensemble averages in [9]. In this note we show that some of these relations hold recurrently, and provide explicit estimates for the time intervals of recurrence which are independent of the solution.
Citation: C. Foias, M. S Jolly, O. P. Manley. Recurrence in the 2-$D$ Navier--Stokes equations. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 253-268. doi: 10.3934/dcds.2004.10.253
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