LARGE GLOBAL SOLUTIONS FOR THE ENERGY-CRITICAL NONLINEAR SCHRODINGER EQUATION

In this work, we consider the three-dimensional defocusing energy-critical nonlinear Schr & ouml;dinger equation i partial derivative(t)u + Delta u = |u|(4)u, (t, x) is an element of R x R-3 . Applying the incoming and outgoing decomposition presented in the recent work [M. Beceanu, Q. Deng, A. Soffer, and Y. Wu, Comm. Math. Phys., 382 (2021), pp. 173-237], we prove that for any radial function f with chi <= 1 f is an element of Pi(1) and chi >= 1 f is an element of Pi(0) with 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.