7 problems

Stability-scaling conjecture. Singularities with space-time scaling that does not correspond to the stability scaling of these schemes would require a different method.

A vortex sheet is a solution of the two-dimensional incompressible Euler equation whose velocity field is discontinuous across an interface; here the initial interface data are ass…

Marchioro–Pulvirenti conjecture. The set of collapses ${\mathfrak C}$ has Lebesgue measure $0$.

Let $\bar\rho$ and $u$ be a smooth solution of the isentropic hyperbolic system … … with $p=\bar\rho^\gamma$, $\gamma>1$, and constant $c$. Finite-time vacuum conjecture. If there…

Let $\rho(t)$ be the solution on the one-dimensional torus $\mathbb T$, and let $T$ denote a possible singularity time. The numerical simulations consider the convex mobility…

Consider a water-wave solution whose fluid interface is initially a graph. Castro–Córdoba–Fefferman–Gancedo–Gómez-Serrano conjecture. There exists at least one such solution for wh…

Adiabatic shrinking conjecture. Large-energy, degree-one initial data develop singularities in finite time, and the singularity formation has the universal form of adiabatic shrink…