Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data
Blowup of classical solutions for a class of 3-D quasilinear wave equations with small initial data
This paper mainly concerns with the small data solution problem for the 3-D nonlinear wave equation: $\partial_t^2u-(1+u+\partial_t u)\Delta u=0$. This equation is prototypical of the more general equation $$ \sum_{i,j=0}^3g_{ij}(u, \nabla u)\partial_{ij}^2u =0 , $$ where $x_0=t$, $\nabla=(\partial_0, \partial_1, ..., \partial_3)$, and $$ g_{ij}(u, \nabla u)=c_{ij}+d_{ij}u+ \sum_{k=0}^3e_{ij}^k\partial_ku+O(|u|^2+|\nabla u|^2) $$ are …