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
Kunio Hidano, Chengbo Wang, and Kazuyoshi Yokoyama
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
Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703087
Mathematical Reviews number (MathSciNet)
MR2919103
Zentralblatt MATH identifier
1269.35019
Subjects
Primary: 35L15: Initial value problems for second-order hyperbolic equations 35L72: Quasilinear second-order hyperbolic equations
Citation
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
