We obtain the global well-posedness and scattering for the radial solution to the defocusing
conformal invariant nonlinear wave equation with initial data in the critical Besov space
. This is the
-dimensional
analogue of Dodson’s result (2019), which was the first on the global well-posedness
and scattering of the energy subcritical nonlinear wave equation without the uniform
boundedness assumption on the critical Sobolev norms employed as a substitute of
the missing conservation law with respect to the scaling invariance of the equation.
The proof is based on exploiting the structure of the radial solution, developing the
Strichartz-type estimates and incorporation of Dodson’s strategy (2019), where we
also avoid a logarithm-type loss by employing the inhomogeneous Strichartz
estimates.
