3 problems

Global scattering theorem. In the four sign regimes, the following conclusions hold: if $\mu_1=\mu_2=-1$, then $u$ is global and scatters; if $\mu_1=1$ and $\mu_2=-1$, then $u$ is…

Global wellposedness conjecture. When $\mu=1$, the equation is globally wellposed: for each $u_0\in\Sigma$ there is a unique global solution…

Cazenave–Kenig–Merle conjecture. When $\mu=1$, solutions exist globally and scatter: for every $u_0\in\dot{H}^1(\mathbb{R}^d)$, there is a unique global solution…