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LARGE GLOBAL SOLUTIONS FOR ENERGY-CRITICAL NONLINEAR SCHR ¨ODINGER EQUATION

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LARGE GLOBAL SOLUTIONS FOR ENERGY-CRITICAL NONLINEAR SCHR ¨ODINGER EQUATION

RUOBING BAI

CENTER FOR APPLIED MATHEMATICS TIANJIN UNIVERSITY

TIANJIN 300072, CHINA

In this work, we consider the 3D defocusing energy-critical nonlinear Schr¨odinger equa- tion

i∂tu+ ∆u=|u|4u, (t, x)∈R×R3.

Applying the outgoing and incoming decomposition presented in the recent work [1], we prove that any radial function f with χ≤1f ∈ H1 and χ≥1f ∈ Hs0 with 56 < s0 < 1, there exists an outgoing component f+ (or incoming component f−) of f, such that when the initial data isf+, 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.

References

[1] M. Beceanu, Q. Deng, A. Soffer and Y. Wu, Large global solutions for nonlinear Schr¨odinger equations II, mass-supercritical, energy-subcritical cases, Commu. Math. Phy., 382 (1), 2021, 173-237.

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