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

Abstract

In this paper, we study the defocusing energy-critical nonlinear Schrödinger 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.

43 pages. arXiv admin note: text overlap with arXiv:2110.11648

References in corpus (3)

• Ill-posedness for nonlinear Schrodinger and wave equations
• Almost sure scattering for the radial energy critical nonlinear wave equation in three dimensions
• Almost sure local well-posedness for the supercritical quintic NLS