Scattering for Stochastic Nonlinear Schrödinger Equations with additive noise
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909415973584896 |
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| author | Başakoğlu, Engin Temur, Faruk Yeşiloğlu, Barış Yılmaz, Oğuz |
| author_facet | Başakoğlu, Engin Temur, Faruk Yeşiloğlu, Barış Yılmaz, Oğuz |
| contents | We study the scattering for the energy-subcritical stochastic nonlinear Schrödinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise $ϕ(x)g(t,ω)dB(t,ω)$ formed by a Schwartz function $ϕ$, and an adapted process $g(t,ω)$ satisfying certain decay. Essentially, the aim of the current paper is to prove almost sure scattering in the spaces $L^2$ and the pseudo-conformal space $Σ$ for an initial data in $Σ$; also in $H^1$ for an initial data in $H^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03469 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering for Stochastic Nonlinear Schrödinger Equations with additive noise Başakoğlu, Engin Temur, Faruk Yeşiloğlu, Barış Yılmaz, Oğuz Analysis of PDEs Probability {35Q55, 35P25, 60H15 We study the scattering for the energy-subcritical stochastic nonlinear Schrödinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise $ϕ(x)g(t,ω)dB(t,ω)$ formed by a Schwartz function $ϕ$, and an adapted process $g(t,ω)$ satisfying certain decay. Essentially, the aim of the current paper is to prove almost sure scattering in the spaces $L^2$ and the pseudo-conformal space $Σ$ for an initial data in $Σ$; also in $H^1$ for an initial data in $H^1$. |
| title | Scattering for Stochastic Nonlinear Schrödinger Equations with additive noise |
| topic | Analysis of PDEs Probability {35Q55, 35P25, 60H15 |
| url | https://arxiv.org/abs/2412.03469 |