Vol. 305, No. 1, 2020

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The global well-posedness and scattering for the $5$-dimensional defocusing conformal invariant NLW with radial initial data in a critical Besov space

Changxing Miao, Jianwei Yang and Tengfei Zhao

Vol. 305 (2020), No. 1, 251–290
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 1,13 ×1,12(5). 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
nonlinear wave equation, Strichartz estimates, scattering, hyperbolic coordinates, Morawetz estimates
Mathematical Subject Classification 2010
Primary: 35B40, 35L05
Secondary: 35Q40
Milestones
Received: 25 June 2018
Accepted: 31 October 2019
Published: 17 March 2020
Authors
Changxing Miao
Institute of Applied Physics and Computational Mathematics
Beijing
China
Jianwei Yang
Beijing Institute of Technology
Beijing
China
Tengfei Zhao
Beijing Computational Science Research Center
Beijing
China