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arXiv · 2111.11935

Almost sure scattering for the nonradial energy-critical NLS with arbitrary regularity in 3D and 4D cases

Jia Shen·Avy Soffer·Yifei Wu
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Abstract

In this paper, we study the defocusing energy-critical nonlinear Schr\"odinger equations $$ i\partial_t u + \Delta u = |u|^{\frac{4}{d-2}} u. $$ When $d=3,4$, we prove the almost sure scattering for the equations with non-radial data in $H_x^s$ for any $s\in\mathbb{R}$. In particular, our result does not rely on any spherical symmetry, size or regularity restrictions.

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Jia Shen, Avy Soffer, Yifei Wu. 2021-11-23. Almost sure scattering for the nonradial energy-critical NLS with arbitrary regularity in 3D and 4D cases. https://arxiv.org/abs/2111.11935

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