Special Session 130: 

On a stochastic coupled Kuramoto-Sivashinsky and Ginzburg-Landau-type model driven by multiplicative noises for Marangoni convection

Wei Wu
Qingdao agricultural university
Peoples Rep of China
Co-Author(s):    
Abstract:
Marangoni convection refers to the motion of the fluid driven by the variation of surface tension caused by the variation of surface tension of a liquid with temperature or with the concentration of a surfactant, which has important applications in engineer fields. The coupled Kuramoto-Sivashinsky and Ginzburg-Landau-type ($KS-GL$) model derived by Golovin \emph{et al.} is one of important work for researching Marangoni convection. This model is different from other models for it aims at capturing important features and is simplified, more amenable to analysis. Recently, the mathematical analysis on the coupled $KS-GL$ system has been developed. Duan \emph{et al.} proved existence and uniqueness of global solutions of the coupled $KS-GL$ system. Wu \emph{et al.} proved global well-posedness of the stochastic coupled $KS-GL$ system driven by additive noises. In this talk, we present global well-posedness on the stochastic coupled $KS-GL$ system driven by multiplicative noises. Using the transformation of exponential functionals of Brownian motions, we turn the stochastic system into a random PDE system, then by applying the contraction mapping principle we prove the local well-posedness result and at last, we establish \textit{ priori} energy estimates which ensure the existence of global solutions.