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arXiv · 2212.06487

Global Well-posedness for the Biharmonic Quintic Nonlinear Schr\"odinger Equation on $\mathbb{R}^2$

Engin Başakoğlu·T. Burak Gürel·Oğuz Yılmaz
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Abstract

We prove that the Cauchy problem for the 2D quintic defocusing biharmonic Schr\"odinger equation is globally well-posed in the Sobolev spaces $H^s(\mathbb{R}^2)$ for $\frac{8}{7}<s<2$. Our main ingredient to establish the result is the $I$-method of Colliander-Keel-Staffilani-Takaoka-Tao \cite{colliander2002almost} which is used to construct the modified energy functional that is almost conserved in time.

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Engin Başakoğlu, T. Burak Gürel, Oğuz Yılmaz. 2022-12-13. Global Well-posedness for the Biharmonic Quintic Nonlinear Schr\"odinger Equation on $\mathbb{R}^2$. https://arxiv.org/abs/2212.06487

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