5 problems

Let $\psi_1(x,y,t)$ and $\psi_2(x,y,t)$ be solutions of the two-dimensional Navier–Stokes equation for turbulent Kolmogorov flow with an even forcing wavenumber $n_K$, subject to t…

Sharp decay-rate conjecture. The sharp decay rate of one derivative of this profile should be close to $t^{-3/2}$ rather than $t^{-1.2}$.

Beck–Wayne conjecture. When $\nu$ is sufficiently small, the perturbation decays at the rate

Let a perturbation of the Kolmogorov flow evolve in the stable case, with viscosity coefficient $\nu>0$ sufficiently small. Beck–Wayne's enhanced dissipation conjecture. The pertur…

Let $\omega$ solve the full linearized Navier–Stokes equation around the Kolmogorov flow $V_{NS}=(-a_0e^{-\nu t}\cos y,0)$, namely … with … The vorticity satisfies the same enhance…