Blowup of small data solutions for a class of quasilinear wave equations in two dimensions: an outline of the proof

Abstract

We consider here quasilinear wave equations in R ²⁺¹

$$ \partial _t^2 u - \Delta _x u + \sum\limits_{0 \leqslant i,j \leqslant 2} {g_{ij} \left( {\nabla u} \right)} \,\partial _{ij}^2 u = 0 $$

((0.1))

where

$$ x_0 = t,\,x = \left( {x_1 ,x_2 } \right),\,g_{ij} = g_{ji} ,\,g_{ij} \left( 0 \right) = 0 $$

.