Large Global Solutions for the Energy-Critical Nonlinear Schrödinger Equation

Abstract

In this work, we consider the three-dimensional defocusing energy-critical nonlinear Schrödinger equation . 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 with and with , there exists an outgoing component (or incoming component ) of , such that when the initial data is , then the corresponding solution is globally well-posed and scatters forward in time; when the initial data is , then the corresponding solution is globally well-posed and scatters backward in time.

Locations

• arXiv (Cornell University) - View - PDF
• SIAM Journal on Mathematical Analysis - View