Global existence for small data Cauchy problem of semilinear wave equations with scaling invariant damping in 3-D is established in this work, assuming that the data are radial and the constant in front of the damping belongs to $[1.5,2)$. The proof is based on a weighted $L^2-L^2$ estimate for inhomogeneous wave equation, which is established by interpolating between energy estimate and a Morawetz type estimate.

中文翻译：

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具有3-D比例不变阻尼的半线性波动方程的整体存在

假设数据是径向的且阻尼前的常数属于，则建立了3-D尺度不变阻尼的半线性波动方程的柯西问题。 $[\mathrm{1个}。5，\mathrm{2个}）$。证明是基于加权的${\mathrm{大号}}^{\mathrm{2个}}-{\mathrm{大号}}^{\mathrm{2个}}$ 非均质波动方程的估计，该方程是通过在能量估计和Morawetz类型估计之间进行插值而建立的。