5 problems

Yakhot's conjecture. In the hydrodynamic limit, the probability distribution of the Kuramoto–Sivashinsky equation may be mimicked by that of the noise-driven inviscid Burgers equat…

Let $\Phi^\infty$ be the limiting flow kernel and fixed point of the stochastic RG operator $\mathfrak{R}$, so that … The limiting kernel represents the vanishing-regularization li…

Local dissipativity conjecture. The limit probability measures of the theorem are supported not only on weak Euler solutions but in fact on solutions which are locally dissipative.

Let $Q_b(x_w,t_w)$ be the renormalized probability quantity in the RG flow, with rescaling parameter $b$, and suppose that for $b\gg 1$ it has the exponential asymptotic form … Her…

Let $\theta_0$ be initial data for an active scalar, and suppose that spontaneous stochasticity occurs for the associated limiting particle trajectories \tilde{\text{\boldmath xi…