報(bào) 告 人：張登 長(zhǎng)聘副教授

報(bào)告題目：The three dimensional stochastic Zakharov system

報(bào)告時(shí)間：2024年5月25日（周六）下午4:00

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1709學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)研究院、數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

       張登，上海交通大學(xué)數(shù)學(xué)科學(xué)學(xué)院長(zhǎng)聘副教授，博士生導(dǎo)師，獲得國(guó)家自然科學(xué)基金優(yōu)青項(xiàng)目、上海市啟明星項(xiàng)目等資助。張登主要從事隨機(jī)偏微分方程及其相關(guān)領(lǐng)域的研究，在隨機(jī)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(guān)成果發(fā)表在A(yíng)OP, ARMA, CMP, JMPA, PTRF, TAMS等國(guó)際期刊。

報(bào)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.