Title: Almost global existence for 3-d systems of nonlinear wave equations

Abstract:  In this joint work with Taylor Rhoads, we combine a space-time Klainerman-Sobolev estimate with an adaptation of Dafermos and Rodnianski’s $r^p$-weighted local energy estimate to establish almost global existence for quasilinear wave equations with small initial data.  The nonlinearity $Q(u,\partial u, \partial^2 u)$, which vanishes to second order, is permitted to depend on the solution, not just its derivatives.  And we assume $(\partial_u^2 Q)(0,0,0)=0$.  The almost global result that is obtained is an analog of that proved by Lindblad for scalar equations.