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In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schrödinger equation $$\begin{aligned} i\partial _t u + \varDelta u - |x|^{-b} |u|^\alpha u = 0, \quad u(0)=u_0 \in H^1, \end{aligned}$$i∂tu+Δu-|x|-b|u|αu=0,u(0)=u0∈H1,with $$b, \alpha >0$$b,α>0. We first study the decaying property of global solutions for the equation when $$0<\alpha <\alpha ^\star $$0<α<α⋆ where $$\alpha ^\star = \frac{4-2b}{d-2}$$α⋆=4-2bd-2 for $$d\ge 3$$d≥3. The proof makes use of an argument of Visciglia (Math Res Lett 16(5):919–926, 2009). We next use this decay to show the energy scattering for the equation in the case $$\alpha _\star<\alpha <\alpha ^\star $$α⋆<α<α⋆, where $$\alpha _\star = \frac{4-2b}{d}$$α⋆=4-2bd.

Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation