### On almost global existence and local well posedness for some 3-D quasi-linear wave equations

#### Abstract

We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the almost global existence of a strong solution for every small initial data in $H^2 \times H^1$. We also show that the initial-value problem is locally well posed.

#### Article information

Source
Adv. Differential Equations, Volume 17, Number 3/4 (2012), 267-306.

Dates
First available in Project Euclid: 17 December 2012