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<p>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, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n\ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Edison Cuba,
  • Lucas C. F. Ferreira

摘要

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, \(n\ge 3\) 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.