2 problems

Let $\mathcal{X}=(\{v\leq 0\}\cup \{t\leq -0.9\})\cap\{-1\leq u<0\}$ and let $\mathcal{C}$ be the backward light cone. Let $\phi$ solve the relevant wave-map or semilinear equation…

Critical norm conjecture. Then $u$ is global and scatters: there exist unique $(u_0^{\pm},u_1^{\pm})\in\dot{H}^{s_c}_x(\mathbb{R}^d)\times\dot{H}^{s_c-1}(\mathbb{R}^d)$ such that