The weak null condition and global existence using the p-weighted energy method

Understand

We prove global existence for solutions arising from small initial data for a large class of quasilinear wave equations satisfying the `weak null condition' of Lindblad and Rodnianski, significantly enlarging upon the class of equations for which global existence is known.

• In addition to the usual weak null condition, we require a certain hierarchical structure in the semilinear terms.
• Included in this class are the Einstein equations in harmonic coordinates, so a special case of our results is a new proof of the stability of Minkowski space.
• Our proof also applies to the coupled Einstein-Maxwell system in harmonic coordinates and Lorenz gauge, as well as to various model scalar wave equations which do not satisfy the null condition.