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

Kunio Hidano; Chengbo Wang; Kazuyoshi Yokoyama

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

Analysis of PDEs 2012-04-04 v2

Authors: Kunio Hidano , Chengbo Wang , 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.

Keywords

quasi-linear wave equation almost global existence local well-posedness low-regularity data Cauchy problem space-time L^2 estimate radial symmetry

Cite

@article{arxiv.1004.3349,
  title  = {On almost global existence and local well-posedness for some 3-D quasi-linear wave equations},
  author = {Kunio Hidano and Chengbo Wang and Kazuyoshi Yokoyama},
  journal= {arXiv preprint arXiv:1004.3349},
  year   = {2012}
}

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

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

Abstract

Keywords

Cite

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