Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866915124331151360 |
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| author | Yu, Xueying |
| author_facet | Yu, Xueying |
| contents | In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a solution remains bounded in $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$ in its maximal interval of existence, then the interval is infinite and the solution scatters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1805_03230 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$ Yu, Xueying Analysis of PDEs In this paper we consider the Cauchy initial value problem for the defocusing quintic nonlinear Schrödinger equation in $\mathbb{R}^2$ with general data in the critical space $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$. We show that if a solution remains bounded in $\dot{H}^{\frac{1}{2}} (\mathbb{R}^2)$ in its maximal interval of existence, then the interval is infinite and the solution scatters. |
| title | Global well-posedness and scattering for the defocusing $\dot{H}^{\frac{1}{2}}$-critical nonlinear Schrödinger equation in $\mathbb{R}^2$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1805.03230 |