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arXiv · 2412.03469

Scattering for Stochastic Nonlinear Schr\"odinger Equations with additive noise

Engin Başakoğlu·Faruk Temur·Barış Yeşiloğlu·Oğuz Yılmaz
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Abstract

We study the scattering for the energy-subcritical stochastic nonlinear Schr\"odinger equation (SNLS) with additive noise. In particular, we examine the long-time behavior of solutions associated with the noise $\phi(x)g(t,\omega)dB(t,\omega)$ formed by a Schwartz function $\phi$, and an adapted process $g(t,\omega)$ 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 $\Sigma$ for an initial data in $\Sigma$; also in $H^1$ for an initial data in $H^1$.

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Engin Başakoğlu, Faruk Temur, Barış Yeşiloğlu, Oğuz Yılmaz. 2024-12-04. Scattering for Stochastic Nonlinear Schr\"odinger Equations with additive noise. https://arxiv.org/abs/2412.03469

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