南京大学 学术报告（09.26）张登：The three dimensional stochastic Zakharov system

报告人：张登  教授（上海交通大学）

时 间：2024年9月26日

地 点：南京大学鼓楼校区西大楼 210

摘 要：This talk is concerned with recent results for the three dimensional stochastic Zakharov system in the energy space, which couples a stochastic Schroedinger equation driven by linear multiplicative noise and a stochastic wave equation with additive noise. We will show the well-posedness of this system up to the maximal existence time and provide a blow-up alternative. The global existence of solutions below the ground state is also derived. Furthermore, we present a noise regularization result on finite time blowup before any given time. Two main ingredients of the 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, which can control Schroedinger equations with derivative perturbations arising from the noise. Another key point for the noise regularization effect is a Strichartz estimate for the Schroedinger equation with a potential solving the free wave equation. This work is in joint with Sebastian Herr, Michael Roeckner and Martin Spitz.

报告人简介： 张登，上海交通大学数学科学学院教授，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。

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