A note on quasilinear wave equations in two space dimensions II: Almost global existence of classical solutions

We give an alternative proof of Alinhac's almost global existence result for the Cauchy problem of quasilinear wave equations with quadratic nonlinearity satisfying the null condition in 2-D (S. Alinhac, 2001, [3]). The main innovation of our proof is that the Lorentz boost operator is not employed in the generalized energy estimates.