Abstract

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 ${Ḃ}_{1,1}^3\times {Ḃ}_{1,1}^2\left({ℝ}^5\right)$. This is the $5$-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.

Keywords

Mathematical Subject Classification 2010

Milestones

Authors