Georgia Institute of Technology College of Sciences

We study the sharp asymptotics for a class of quasilinear wave equations satisfying a weak null condition but not the classical null condition in three spatial dimensions. We prove that the asymptotics are very different from those for the equations satisfying the classical null condition. In particular, at leading order, the solution displays a continuous superposition of decay rates.

Moreover, we show that any solution that decays faster than expected in a compact spatial region must vanish identically. The talk is based on joint work in progress with Jonathan Luk and Dongxiao Yu.