7 problems

Cauchy-horizon conjecture. The perturbed solution has a Cauchy horizon that is a perturbation of the Cauchy horizon of the background solution.

Crease-and-singular-boundary conjecture. The perturbed solution has a crease and singular boundary that are perturbations of the crease and singular boundary of the background solu…

Time-of-first-blowup conjecture. The perturbed solution forms a shock at a time that is a perturbation of $T_{\mathrm{Shock}}$; its first blowup time is the smallest value of $t$ a…

Let $d\geq 2$ and consider a $d$-dimensional nonlinear symmetric system that is totally linearly degenerate. Suppose the initial data belong to $H^s(\mathbb{R}^d)$ with…

Let $u_0\in L^2(\mathbb{R})$ be smooth initial data with a single hump for the defocusing modified fractional Korteweg–de Vries equation, with dispersion parameter $\alpha$. Defocu…

Pearcey asymptotics conjecture. Near the first singularity, the solution has the asymptotic expansion

First-singularity conjecture. Spherically symmetric solutions of this equation have their first singularities on the event horizon $\mathcal{H}^{+}$.