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arXiv · 1507.05908

Determining modes for the 3D Navier-Stokes equations

Alexey Cheskidov·Mimi Dai·Landon Kavlie
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Abstract

We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blows up, its time average is uniformly bounded for all solutions on the global attractor. The bound is compared to Kolmogorov's dissipation wavenumber and the Grashof constant.

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Alexey Cheskidov, Mimi Dai, Landon Kavlie. 2015-07-21. Determining modes for the 3D Navier-Stokes equations. https://doi.org/10.1016/j.physd.2017.11.014

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