報 告 人：張登 長聘副教授

報告題目：The three dimensional stochastic Zakharov system

報告時間：2024年5月25日（周六）下午4:00

報告地點：靜遠樓1709學術報告廳

主辦單位：數學研究院、數學與統計學院、科學技術研究院

報告人簡介：

       張登，上海交通大學數學科學學院長聘副教授，博士生導師，獲得國家自然科學基金優青項目、上海市啟明星項目等資助。張登主要從事隨機偏微分方程及其相關領域的研究，在隨機薛定諤方程的全局適定性、多波包爆破解和多孤波解，流體方程的弱解非唯一性等方面取得了研究成果，相關成果發表在AOP, ARMA, CMP, JMPA, PTRF, TAMS等國際期刊。

報告摘要：

       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.