One Remark on Barely \dot{H}^{s_{p}} Supercritical Wave Equations

Details One Remark on Barely \dot{H}^{s_{p}} Supercritical Wave Equations One Remark on Barely \dot{H}^{s_{p}} Supercritical Wave Equations

2009-05-30

arxiv.org/abs/0906.0044v2

Mathematics

Analysis of PDEs

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Scientific paper

We prove that a good \dot{H}^{s_{p}} critical theory for the 3D wave equation \partial_{tt} u - \triangle u = -|u|^{p-1} u can be extended to prove global well-posedness of smooth solutions of at least one 3D barely \dot{H}^{s_{p}} supercritical wave equation \partial_{tt} u - \triangle u =- |u|^{p-1} u g(|u|), with g growing slowly to infinity, provided that a Kenig-Merle type condition is satisfied. This result extends those obtained for the particular case s_{p}=1.

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