Global Well-posedness for the Biharmonic Quintic Nonlinear Schr\"odinger Equation on $\mathbb{R}^2$
Analysis of PDEs
2023-05-02 v2 Mathematical Physics
math.MP
Abstract
We prove that the Cauchy problem for the 2D quintic defocusing biharmonic Schr\"odinger equation is globally well-posed in the Sobolev spaces for . Our main ingredient to establish the result is the -method of Colliander-Keel-Staffilani-Takaoka-Tao \cite{colliander2002almost} which is used to construct the modified energy functional that is almost conserved in time.
Keywords
Cite
@article{arxiv.2212.06487,
title = {Global Well-posedness for the Biharmonic Quintic Nonlinear Schr\"odinger Equation on $\mathbb{R}^2$},
author = {Engin Başakoğlu and T. Burak Gürel and Oğuz Yılmaz},
journal= {arXiv preprint arXiv:2212.06487},
year = {2023}
}