Determining modes for the 3D Navier-Stokes equations

Published 21 Jul 2015 in math.AP | (1507.05908v2)

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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