  This work concerns the semilinear wave equation in three space dimensions
with a power-like nonlinearity which is greater than cubic, and not quintic
(i.e. not energy-critical). We prove that a scale-invariant Sobolev norm of any
non-scattering solution goes to infinity at the maximal time of existence. This
gives a refinement on known results on energy-subcritical and
energy-supercritical wave equation, with a unified proof.
  The proof relies on the channel of energy method, as in arXiv:1204.0031, in
weighted scale-invariant Sobolev spaces which were introduced in
arXiv:1506.00788. These spaces are local, thus adapted to finite speed of
propagation, and related to a conservation law of the linear wave equation. We
also construct the adapted profile decomposition.
