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

Terence Tao

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

Terence Tao

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Abstract

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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Terence Tao. 2006-06-07. Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data. https://arxiv.org/abs/math/0606145

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