Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations

Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions.