Advances in Differential Equations
- Adv. Differential Equations
- Volume 17, Number 3/4 (2012), 267-306.
On almost global existence and local well posedness for some 3-D quasi-linear wave equations
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.
Adv. Differential Equations, Volume 17, Number 3/4 (2012), 267-306.
First available in Project Euclid: 17 December 2012
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Hidano, Kunio; Wang, Chengbo; Yokoyama, Kazuyoshi. On almost global existence and local well posedness for some 3-D quasi-linear wave equations. Adv. Differential Equations 17 (2012), no. 3/4, 267--306. https://projecteuclid.org/euclid.ade/1355703087