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arXiv · 2308.06210

Global Well-posedness for The Fourth-order Nonlinear Schr\"{o}dinger Equations on $\mathbb{R}^{2}$

Engin Başakoğlu·Barış Yeşiloğlu·Oğuz Yılmaz
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Abstract

We study the global well-posedness of the two-dimensional defocusing fourth-order Schr\"odinger initial value problem with power type nonlinearities $\vert u\vert^{2k}u$ where $k$ is a positive integer. By using the $I$-method, we prove that global well-posedness is satisfied in the Sobolev spaces $H^{s}(\mathbb{R}^{2})$ for $2-\frac{3}{4k}<s<2$.

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Engin Başakoğlu, Barış Yeşiloğlu, Oğuz Yılmaz. 2023-08-11. Global Well-posedness for The Fourth-order Nonlinear Schr\"{o}dinger Equations on $\mathbb{R}^{2}$. https://arxiv.org/abs/2308.06210

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