  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.
