Random attractors for damped stochastic fractional Schrödinger equation on $\mathbb{R}^{n}$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915193493127168 |
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| author | Lin, Li Zhang, Yanjie Zhang, Ao |
| author_facet | Lin, Li Zhang, Yanjie Zhang, Ao |
| contents | We study the random attractors associated with the stochastic fractional Schrödinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schrödinger equation with Gaussian noise, we show the existence and uniqueness of a global solution to the damped stochastic fractional nonlinear Schrödinger equation in $H^α(\mathbb{R}^n)$. Furthermore, we demonstrate that this equation defines an infinite-dimensional dynamical system, which possesses a global attractor in $H^α(\mathbb{R}^n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17151 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Random attractors for damped stochastic fractional Schrödinger equation on $\mathbb{R}^{n}$ Lin, Li Zhang, Yanjie Zhang, Ao Analysis of PDEs We study the random attractors associated with the stochastic fractional Schrödinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schrödinger equation with Gaussian noise, we show the existence and uniqueness of a global solution to the damped stochastic fractional nonlinear Schrödinger equation in $H^α(\mathbb{R}^n)$. Furthermore, we demonstrate that this equation defines an infinite-dimensional dynamical system, which possesses a global attractor in $H^α(\mathbb{R}^n)$. |
| title | Random attractors for damped stochastic fractional Schrödinger equation on $\mathbb{R}^{n}$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.17151 |