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

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

2010-04-20

arxiv.org/abs/1004.3349v2

Advances in Differential Equations, 17(2012), No. 3-4, 267-306

Mathematics

Analysis of PDEs

34 pages, final version, to appear in Advances in Differential Equations

Scientific paper

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.

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