Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℝ³

Downloads

Abstract

The main purpose of the present paper is to consider the well-posedness of the L2-critical nonlinear Schrödinger equation of a Hartree type

ð’¾âˆ‚tψ + △ψ = (|x|−1 ∗ |ψ|8/3)ψ,      (t, x) ∈ â„+ × â„3.

More precisely, we shall establish the local existence of solutions for initial data ψ0 in L2(â„3), as well as the existence of global solutions for small initial data. Moreover, we shall prove the existence of scattering operator.

Keywords

Nonlinear Schrödinger equation , power convolution , Hartree equation , local and global existence
  • George Venkov Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8 "Kliment Ohridski" Str., 1756 Sofia, Bulgaria.
  • Pages: 15–28
  • Date Published: 2009-09-01
  • Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

Downloads

Download data is not yet available.

Published

2009-09-01

How to Cite

[1]
G. Venkov, “Small Data Global Existence and Scattering for the Mass-Critical Nonlinear Schrödinger Equation with Power Convolution in ℝ³”, CUBO, vol. 11, no. 4, pp. 15–28, Sep. 2009.

Issue

Vol. 11 No. 4 (2009): CUBO, A Mathematical Journal

Section

Articles