6 problems

Let the periodic channel be ${\mathbb T}\times{\mathbb R}$, and consider the linearised Euler--Boussinesq system near the constantly stratified Couette flow … Here…

Let $\beta$ denote the exponent governing the asymptotic stability threshold for a symmetric flow, under either the non-slip or Navier-slip boundary condition. Asymptotic stability…

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

High-Reynolds-number damping conjecture. For high-Reynolds-number flows, an appropriate analogue of Theorem should hold for initial data

Generic inviscid damping conjecture. In regularities lower than Gevrey-$2$—with $H^s$ for $s>3/2$ suggested as one natural choice—“most” sufficiently small initial data should damp…

For a two-dimensional Euler shear flow, let $\omega^R_{in}$ and $\omega_{in}^{\nu}$ be components of the initial vorticity, with the first having Gevrey-$\frac{1}{s}$ regularity un…