16 problems

Large-scale convergence conjecture. Under the scaling assumption on the noise, the expected density should satisfy

Let ${\bf g}_{M,a}$ be a subextremal Kerr metric. Let $(\Sigma_0,g_0,k_0)$ be a suitably small perturbation of its initial data, where $\Sigma_0$ is a 3-dimensional manifold, $g_0$…

Singular-limit conjecture. The local model is the singular limit of the non-local model as $\mu\to\delta_{0^{+}}$.

Let the delay kernel $\alpha(t)$ converge to the Dirac mass $\delta(t-d)$ in the sense of distributions. Delayed-limit convergence conjecture. Solutions of the delayed equations sh…

Let $\alpha(t)$ be a delay kernel converging to the Dirac mass $\delta(t)$, and let $X(t)$ be the total activity of the delayed equation while $N(t)$ is the discharging flux of the…

Let $\alpha(t)$ converge to $\delta(t-d)$ in the sense of distributions, where $d$ is the delay, and let $X(t)$ be the total activity in the delayed equation. Delayed branch-select…

Let the instantaneous transmission model have multiple local solution branches for the same initial condition, corresponding to multiple possible values of $N(0)$. Let the delay ke…

Let $N$ coaxial vortex rings have cylindrical-coordinate positions…

Consider the one-dimensional Dirichlet problem … with the Dirichlet boundary conditions and initial data specified in the paper, and let $u$ denote its solution. Large-population w…

Convergence conjecture. One may conjecture that

Eady slice hydrostatic limit conjecture. Weak solutions of the Eady-Boussinesq vertical slice equations converge to weak solutions of the semi-geostrophic Eady slice equations as…

Global-diagram convergence conjecture. Even the global bifurcation diagram could be captured asymptotically by a convergence rate towards the singular limit.

Point-vortex limit conjecture. A massive particle moves according to

Let $\rho^\alpha$, $u^\alpha$, and $c^\alpha$ solve the lower-order approximation … where $alpha>0$, and let the NSK system be the corresponding Navier–Stokes–Korteweg system. Rohd…

Assume the hypotheses of Proposition. Let $\omega^\nu(x,t)$ solve the rotating viscous vorticity equation, and let $\epsilon>0$ be sufficiently small. Let $\omega_\epsilon(x)$ be a…

Convergence conjecture. $D^*$ might converge identically to $D^\dagger$ in this singular limit for all frequencies, both small and large. The numerical evidence in Figure 0d sugges…