Global Well-posedness for the Logarithmically Energy-Supercritical Nonlinear Wave Equation with Partial Symmetry

We establish global well-posedness and scattering results for the logarithmically energy-supercritical nonlinear wave equation, under the assumption that the initial data satisfies a partial symmetry condition. These results generalize and extend work of Tao in the radially symmetric setting. The techniques involved include weighted versions of Morawetz and Strichartz estimates, with weights adapted to the partial symmetry assumptions. In an appendix, we establish a corresponding quantitative result for the energy-critical problem.