English

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 Hs(R2)H^s(\mathbb{R}^2) for 87<s<2\frac{8}{7}<s<2. Our main ingredient to establish the result is the II-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}
}