Almost sure well-posedness for the cubic nonlinear Schrödinger equation in the super-critical regime on $\TTT^d$, $d\ge 3$

Abstract

In this paper we prove almost sure local well-posedness in both atomic spaces $X^s$ and Fourier restriction spaces $X^{s,b}$ for the cubic nonlinear Schrödinger equation on $\TTT^d$ ($d\ge 3$) in the super-critical regime.

References in corpus (9)

• Well-posedness and scattering for the KP-II equation in a critical space
• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Almost sure well-posedness of the cubic nonlinear Schrödinger equation below L^2(T)
• Global well-posedness of the energy-critical defocusing NLS on $\mathbb{R}\times {\mathbb{T}}^3$
• Almost sure global well posedness for the radial nonlinear Schrodinger equation on the unit ball I: the 2D case
• Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity
• On the probabilistic well-posedness of the nonlinear Schrödinger equations with non-algebraic nonlinearities
• Almost sure scattering for the energy-critical NLS with radial data below $H^1({\mathbb{R}}^4)$
• Random data final-state problem for the mass-subcritical NLS in $L^2$

Cited by in corpus (2)

• Invariant Gibbs measures and global strong solutions for nonlinear Schrödinger equations in dimension two
• Almost sure global well-posedness for the energy supercritical NLS on the unit ball of ${\mathbb{R}}^3$