Weak pullback 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 |
| Published: |
2024
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| _version_ | 1866915005909172224 |
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| author | Zhang, Ao Zhang, Yanjie Zhai, Sanyang Lin, Li |
| author_facet | Zhang, Ao Zhang, Yanjie Zhai, Sanyang Lin, Li |
| contents | This article discusses the weak pullback attractors for a damped stochastic fractional Schrödinger equation on $\mathbb{R}^n$ with $n\geq 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the existence and uniqueness of a global solution for the systems with the nonlinear term $|u|^{2σ}u$ are proven. Furthermore, we define a mean random dynamical system due to the uniqueness of the solution, which has a unique weak pullback mean random attractor in $L^ρ\left(Ω; L^2\left(\mathbb{R}^n\right)\right)$. This result highlights the long-term dynamics of a broad class of stochastic fractional dispersion equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weak pullback attractors for damped stochastic fractional Schrödinger equation on $\mathbb{R}^n Zhang, Ao Zhang, Yanjie Zhai, Sanyang Lin, Li Analysis of PDEs This article discusses the weak pullback attractors for a damped stochastic fractional Schrödinger equation on $\mathbb{R}^n$ with $n\geq 2$. By utilizing the stochastic Strichartz estimates and a stopping time technique argument, the existence and uniqueness of a global solution for the systems with the nonlinear term $|u|^{2σ}u$ are proven. Furthermore, we define a mean random dynamical system due to the uniqueness of the solution, which has a unique weak pullback mean random attractor in $L^ρ\left(Ω; L^2\left(\mathbb{R}^n\right)\right)$. This result highlights the long-term dynamics of a broad class of stochastic fractional dispersion equations. |
| title | Weak pullback attractors for damped stochastic fractional Schrödinger equation on $\mathbb{R}^n |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.02781 |