8 problems

Ionescu–Iyer–Jia sharp extremal-layer bounds conjecture. The same inequalities should hold with $2^-$ and $1^-$ in place of $7/4$ and $7/8$, respectively. These bounds quantify the…

Bouchet–Morita depletion-property conjecture. The limiting vorticity profile satisfies

Let $U(y)=(U_s(y),0)$ be a smooth shear layer on the half-plane $y\geq 0$, and consider solutions of the linearized incompressible Euler equations satisfying the boundary condition…

Let $G_N\subseteq \mathbb{T}^2$ be the discrete grid used in the paper, let $\rho_0\in L^\infty(G_N)$ be the initial datum, and let the alternating horizontal and vertical wedge fl…

Enhanced-dissipation rate conjecture. For stable monotone shear flows, the enhanced dissipation rate should be $\nu^{1/3}$, and for stable shear flows with a non-degenerate critica…

Let $p=p(n_0)\in(0,1)$ be the exponent in the decay rate from the preceding theorem, where $n_0$ denotes the order of the first nonvanishing derivative of the shear profile. The en…

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…

A three-dimensional shear flow has the form $(U(y),0,W(y))$, where $U$ and $W$ are the streamwise and spanwise velocity profiles. A type I 3D shear is a shear of the type classifie…