In this work, we consider the 3D defocusing energy-critical nonlinear Schrödinger equation $$ i\partial_t u+\Delta u =|u|^4 u, \quad (t,x)\in \mathbb{R}\times \mathbb{R}^3. $$ Applying the outgoing and incoming decomposition presented in the recent work (Beceanu-Deng-Soffer-Wu, 2021), we prove that any radial function $f$ with $\chi_{\leq1}f\in H^1$ and $\chi_{\geq1}f\in H^{s_0}$ with $\frac{5}{6}<s_0<1$, there exists an outgoing component $f_+$ (or incoming component $f_-$) of $f$, such that when the initial data is $f_+$, then the corresponding solution is globally well-posed and scatters forward in time; when the initial data is $f_-$, then the corresponding solution is globally well-posed and scatters backward in time.

This is a joint work with Jia Shen and Yifei Wu.

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