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.

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

References in corpus (2)

• Angular Regularity and Strichartz Estimates for the Wave Equation
• Local Existence for Nonlinear Wave Equation with Radial Data in 2+1 Dimensions

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