Global existence for systems of nonlinear wave equations with bounded, stable asymptotic systems

Understand

Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not.

• The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain systems -- most famously the Einstein equations -- which nevertheless admit global solutions for small initial data.
• The weak null condition has been proposed as a sufficient condition for such a result to hold; it takes the form of a condition on a related set of nonlinear ODEs known as the "asymptotic system".
• Previous results in this direction have required certain structural conditions on the asymptotic system in addition to the weak null condition.