报 告 人：张登 长聘副教授
报告题目：The three dimensional stochastic Zakharov system
报告时间：2024年5月25日（周六）下午4:00
报告地点：静远楼1709学术报告厅
主办单位：数学研究院、数学与统计学院、科学技术研究院
报告人简介：
张登，上海交通大学数学科学学院长聘副教授，博士生导师，获得国家自然科学基金优青项目、上海市启明星项目等资助。张登主要从事随机偏微分方程及其相关领域的研究，在随机薛定谔方程的全局适定性、多波包爆破解和多孤波解，流体方程的弱解非唯一性等方面取得了研究成果，相关成果发表在AOP, ARMA, CMP, JMPA, PTRF, TAMS等国际期刊。
报告摘要：
In this talk , we will show some recent results for the three dimensional stochastic Zakharov system in the energy space, where the Schroedinger equation is driven by linear multiplicative noise and the wave equation is driven by additive noise. We will show the well-posedness of the system up to the maximal existence time and provide a blow-up alternative. We also prove that the solution exists at least as long as it remains below the ground state. Furthermore, we present a noise regularization result on finite time blowup before any given time. Two main ingredients of our proof are the refined rescaling approach and the normal form method. In contrast to the deterministic setting, our functional framework also incorporates local smoothing estimates for Schroedinger equations with derivative perturbations arising from the noise.
