Time-rescaled dynamical convergence to the no-diffusion Kuramoto manifold

Let $W^u(\frac{1}{2\pi})$ be the unstable manifold of the incoherent equilibrium for the diffusive Kuramoto equation, and let $\mathcal M_{0A}$ be the corresponding invariant manifold in the no-diffusion case. Time-rescaled convergence conjecture. After rescaling time by a factor $\frac{1}{K}$, solutions of the equation on $W^u(\frac{1}{2\pi})$ converge to solutions of the no-diffusion equation on $\mathcal M_{0A}$ in Gevrey space on every interval $]-\infty,T]$, with speed $\frac{1}{K}$. The claim concerns the dynamical counterpart of convergence to the Ott–Antonsen manifold and is stated as an unproved conjecture following the formal limiting reduced equation.