报告题目：Stochastic smoothed Zakharov model with mixed multiplicative noise: Analysis and long-time behavior

报 告 人：王凤玲，北京应用物理与计算数学研究所

邀 请 人：刘辉

报告时间：2026年05月16日（星期六）15:10-15:50

报告地点：7JC214

报告摘要：

The analysis of long-time dynamics for nonautonomous stochastic Zakharov systems with nonlinear noise poses significant challenges. To overcome this, we develop a unified framework in Bochner spaces $L^{2p}(\Omega,\mathcal{H})$ for the corresponding smoothed system with regularized nonlinearities. Our approach is based on three key components:

(i) the mixed multiplicative noise (nonlinear in the wave component, linear in the Schrodinger part),

(ii) the truncation technique $\theta_{R}(\cdot)$, and

(iii) spatial regularization achieved through convolution.

Within this framework, we first establish global well-posedness in $C([\tau,\infty),L^{2p}(\Omega,\mathcal{H}))$ for a critical range of $p$, via a unified energy estimate that handles both noise types simultaneously.

Consequently, we prove the existence of a weak pullback mean random attractor in the Bochner space $L^2(\Omega,\mathcal{H})$ for the associated mean random dynamical system. Taken together, these results establish a mean random dynamical theory for such stochastic wave-Schrodinger systems, laying a rigorous foundation for future analysis of their long-time behavior.

报告人简介：王凤玲，女，博士毕业于西南大学和塞维利亚大学（西班牙），现为北京应用物理与计算数学研究所博士后。主要从事无穷维动力系统的渐近行为理论研究，主持中国博士后科学基金项目2项。