We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in both time directions as long as its critical Sobolev norm stays bounded on the maximal interval of existence.

中文翻译：

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散焦能量次临界非线性波动方程的散射

我们在$(1+3)$-维数中考虑散焦功率型非线性波动方程的柯西问题，用于能量亚临界功率$p$ 在$3 < p< 5$ 范围内。我们证明了任何解决方案都是全局时间的，并且只要其临界 Sobolev 范数保持在最大存在间隔上，就会在两个时间方向上散射到自由波。