Special Session 11: Stochastic Partial Differential Equations

Recent progress on stochastic Zakharov system: well-posedness theory and noise-regularization effect
Deng Zhang
Shanghai Jiao Tong University
Peoples Rep of China
Co-Author(s):    
Abstract:
In this talk we will review some recent results on the well-posedness theory and noise-regularization effect for stochastic Zakharov system in dimensions $d\geq 3$. Our focus is particularly directed at the large data regime where the global existence and long-time dynamics of deterministic Zakharov system is largely open. The noise-regularization effect on scattering is proved up to borderlines dictated by the regularity threshold of noise. These works are in joint with Sebastian Herr, Michael Rockner, Martin Spitz and Zhenqi Zhao.