Advances in Differential Equations

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

Kunio Hidano, Chengbo Wang, and Kazuyoshi Yokoyama

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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.


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