# Blowup of small data solutions for a quasilinear wave equation in two space dimensions

### Abstract

For the quasilinear wave equation
$\partial_t^2 u-\Delta u = u_tu_{tt},$
we analyze the long-time behavior of classical solutions with small (not rotationally invariant) data. We give a complete asymptotic expansion of the lifespan and describe the solution close to the blowup point. It turns out that this solution is a “blowup solution of cusp type,” according to the terminology of the author [3].

Serge Alinhac