Remarks on a quasi-linear model of the Navier-Stokes Equations

Details Remarks on a quasi-linear model of the Navier-Stokes Equations Remarks on a quasi-linear model of the Navier-Stokes Equations

2004-09-19

arxiv.org/abs/math/0409310v1

Mathematics

Analysis of PDEs

4 pages

Scientific paper

Dinaburg and Sinai recently proposed a quasi-linear model of the Navier-Stokes equations. Their model assumes that nonlocal interactions in Fourier space are dominant, contrary to the Kolmogorov turbulence phenomenology where local interactions prevail. Their equation corresponds to the linear evolution of small scales on a background field with uniform gradient, but the latter is defined as the linear superposition of all the small scale gradients at the origin. This is not self-consistent.

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