GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL DEFOCUSING NONLINEAR WAVE EQUATION FOR SPHERICALLY SYMMETRIC DATA

摘要

We establish global regularity for the logarithmically energy-supercritical wave equation □u = u5 log(2 + u2) in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.