The global wellposedness and scattering for the $5$D defocusing conformal invariant NLW with radial initial data in a critical Besov space
Abstract
In this paper, we obtain the global wellposedness and scattering for the radial solution to the defocusing conformal invariant nonlinear wave equation with initial data in the critical Besov space $\dot{B}^3_{1,1}\times\dot{B}^2_{1,1}(\mathbb{R}^5)$. This is the five dimensional analogue of \cite{dodson2016}, which is the first result on the global wellposedness 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 Strichartztype estimates and incorporation of the strategy in \cite{dodson2016}, where we also avoid a logarithmtype loss by employing the inhomogeneous Strichartz estimates.
 Publication:

arXiv eprints
 Pub Date:
 February 2018
 arXiv:
 arXiv:1803.00075
 Bibcode:
 2018arXiv180300075M
 Keywords:

 Mathematics  Analysis of PDEs;
 35B40;
 35Q40
 EPrint:
 31pages