Composition estimates and global well-posedness for double-power nonlinear wave equations

This paper aims to establish global well-posedness results for nonlinear wave equations (NLWs) in a broader class of weak-Besov spaces. We consider nonlinearities of both single- and double-power types, and carry out the analysis in higher dimensions, n≥3. To achieve these results, we develop suitable composition-type estimates within our functional framework. These estimates are of independent interest and provide a detailed understanding of how the nonlinearity influences the behavior of solutions in such spaces. In addition, we derive certain time-weighted dispersive estimates for the wave group, which naturally arise in the course of the well-posedness analysis.