The main purpose of the present paper is to consider the well-posedness of the L2-critical nonlinear Schrödinger equation of a Hartree type
𝒾∂tψ + △ψ = (|x|−1 ∗ |ψ|8/3)ψ, (t, x) ∈ ℝ+ × ℝ3.
More precisely, we shall establish the local existence of solutions for initial data ψ0 in L2(ℝ3), as well as the existence of global solutions for small initial data. Moreover, we shall prove the existence of scattering operator.
@article{1450,
title = {Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schr\"odinger Equation with Power Convolution in $\mathbb{R}$$^3$},
journal = {CUBO, A Mathematical Journal},
volume = {11},
year = {2009},
language = {en},
url = {http://dml.mathdoc.fr/item/1450}
}
Venkov, George. Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℝ³. CUBO, A Mathematical Journal, Tome 11 (2009) . http://gdmltest.u-ga.fr/item/1450/