New DNS up to 2048^3 grid points reportedly confirm that perturbations in fully developed turbulence amplify as e^{c sqrt(Re) sqrt(t)}, which is faster than exponential, and saturate quickly.
Nowhere-differentiability of the solution map of 2D Euler equations on bounded spatial domain
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abstract
We consider the incompressible 2D Euler equations on bounded spatial domain $S$, and study the solution map on the Sobolev spaces $H^k(S)$ ($k > 2$). Through an elaborate geometric construction, we show that for any $T >0$, the time $T$ solution map $u_0 \mapsto u(T)$ is nowhere locally uniformly continuous and nowhere Fr\'echet differentiable.
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physics.flu-dyn 1years
2019 1verdicts
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Superfast amplification and superfast nonlinear saturation of perturbations as the mechanism of turbulence
New DNS up to 2048^3 grid points reportedly confirm that perturbations in fully developed turbulence amplify as e^{c sqrt(Re) sqrt(t)}, which is faster than exponential, and saturate quickly.