题目：Well-posedness and large deviations for some stochastic shallow water equations
陈涌，博士，浙江理工大学副教授，硕导。研究兴趣为随机偏微分方程的适定性、大偏差和解的长时间行为。相关成果发表在《J.DifferentialEquations》、《Discrete Contin. Dyn. Syst.》、《Nonlinear Anal.》、《J.Math. Anal.Appl.》、《Potential Anal》、《Stoch Anal Appl》、《中国科学》、《数学年刊》等杂志。
In this talk, we consider the well-posedness and large deviations for stochastic shallow water equations. Firstly, using regularization method and bilinear estimates in Bourgain space, the well-posednesss of stochastic Camassa-Holm equation with additive Wiener noise is established. Secondly, using the weak convergence method, the large deviation for the solutions of stochastic modified Camassa-Holm equation with multiplicative Wiener noise is obtained. Lastly, we consider the well-posedness and large deviation for the solutions of stochastic PDEs with Levy noise. The results can be applied to some types of stochastic shallow water equations, such as stochastic Burgers equation, stochastic b-family equation, stochastic modified Novikov equation and stochastic $\mu$-Hunter-Saxton equation.