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

Abstract

We establish global regularity for the logarithmically energy-supercritical wave equation $\square u=u^5\log (2+u^2)$ 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.

arXiv comment6 pages, no figures. Submitted, J. Hyperbolic Diff. Eq