Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces
Electronic journal of differential equations, Tome 2001 (2001)
In this paper, we study the existence of global solutions to Schrodinger equations in one space dimension with a derivative in a nonlinear term. For the Cauchy problem we assume that the data belongs to a Sobolev space weaker than the finite energy space $H^{1}$. Global existence for $H^{1}$ data follows from the local existence and the use of a conserved quantity. For $H^{s}$ data with s1, the main idea is to use a conservation law and a frequency decomposition of the Cauchy data then follow the method introduced by Bourgain [3]. Our proof relies on a generalization of the tri-linear estimates associated with the Fourier restriction norm method used in [1,25].
@article{EJDE_2001__2001__a202,
author = {Takaoka, Hideo},
title = {Global well-posedness for {Schr\"odinger} equations with derivative in a nonlinear term and data in low-order {Sobolev} spaces},
journal = {Electronic journal of differential equations},
year = {2001},
volume = {2001},
zbl = {0972.35140},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/}
}
TY - JOUR AU - Takaoka, Hideo TI - Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces JO - Electronic journal of differential equations PY - 2001 VL - 2001 UR - http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/ LA - en ID - EJDE_2001__2001__a202 ER -
%0 Journal Article %A Takaoka, Hideo %T Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces %J Electronic journal of differential equations %D 2001 %V 2001 %U http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/ %G en %F EJDE_2001__2001__a202
Takaoka, Hideo. Global well-posedness for Schrödinger equations with derivative in a nonlinear term and data in low-order Sobolev spaces. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a202/