5 problems

Let $u^I$ be a solution to a system of semilinear wave equations whose nonlinearities satisfy the weak null condition: the associated asymptotic system … has a global solution for…

Null-condition well-posedness conjecture. If the null condition holds, then (GNLW) is well-posed in $H^s\times H^{s-1}$ for some $s<\frac n2+\frac34$ when $n=2$, respectively for s…

Weak null condition conjecture. The weak null condition should be sufficient for global existence of solutions arising from sufficiently small and localized initial data.

Let the top-order energy be the highest-order energy associated with a three-dimensional quasilinear wave equation enjoying a weak null structure. Alinhac's blowup-at-infinity conj…

Let $u$ solve a system of semilinear wave equations, and let its reduced system be … The weak null condition means that this reduced system always has global solutions with at most…