Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data

Details Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data

2006-06-07

arxiv.org/abs/math/0606145v1

Mathematics

Analysis of PDEs

6 pages, no figures. Submitted, J. Hyperbolic Diff. Eq

Scientific paper

We establish global regularity for the logarithmically energy-supercritical wave equation $\Box u = u^5 \log(2+u^2)$ in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo \cite{gsv} for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.

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