5 problems

Weak null condition conjecture. The weak null condition is sufficient for global existence of small-data solutions.

Weak null conjecture. The original system of wave equations also admits global solutions for sufficiently small initial data.

Consider the scalar quasilinear wave equation … in $\mathbb{R}^{1+3}_{t,x}$ with small initial data … Here $g^{\alpha\beta}(u)$ are smooth, symmetric coefficients satisfying…

Consider systems satisfying the hierarchical weak null condition, and suppose Condition $1$ is met. Assume also that the linearization around the traveling wave contains no terms o…

Let $u$ solve a quasilinear wave system of the form … with the weak null condition (WNC) defined by the existence of a global asymptotic-PDE solution for the ansatz … whose derivat…