Global existence for a quasilinear wave equation outside of star-shaped domains (Q1597997)

The goal of this paper is to prove global existence of small-amplitude solutions for certain quasilinear Dirichlet-wave equations outside of smooth, compact star-shaped obstacles \({\mathcal K}\subset\mathbb{R}^3\). More precisely the authors deal with smooth quasilinear systems of the form \[ \begin{cases} \partial^2_tu-\Delta u=F(u,Du,D^2u)\quad & (t,x)\in\mathbb{R}_+\times\mathbb{R}^3\setminus {\mathcal K},\\ u(t,\cdot)|_{\partial {\mathcal K}}=0,\quad u(0,\cdot)=g_1,\quad & \partial_tu(0,\cdot)=g_2.\end{cases} \] To this end they use a variation of the conformal method of Christodoulou.