The null condition for quasilinear wave equations in two space dimensions, II
Abstract

Abstract:

We consider quasilinear wave equations with small data of size ε, in two space dimensions. Assuming the null condition is satisfied, we proved in a previous paper the (conjectured) large time existence result. In this paper, using the "geometric blowup" techniques introduced in our previous work, we prove that, under generic conditions on the data, blowup does occur at the specified time; more precisely, the blowup can be described as a "geometric blowup of cusp type" (uniformly in ε in appropriate variables). Taking advantage of the techniques introduced in the paper, we also prove the blowup result for the technically similar case of quasilinear wave equations, without null condition, in three space dimensions.