学术讲座(Michael Röckner 10.8)

英文:Global solutions to random 3D vorticity equations for small initial data 中文:随机三维涡量方程小初值的整体解

发布人:周妍 发布日期:2018-09-18
主题
英文:Global solutions to random 3D vorticity equations for small initial data 中文:随机三维涡量方程小初值的整体解
活动时间
-
活动地址
新数学楼415室
主讲人
Michael Röckner 教授(德国Bielefeld University 和中国科学院数学与系统科学研究院)

摘要:

One proves the existence and uniqueness in Image removed. Image removed., Image removed. Image removed.< p < 2, of a global mild solution to random vorticity equations associated to stochastic 3D Navier-Stokes equations with linear multiplicative Gaussian noise of convolution type, for sufficiently small initial vorticity. This resembles some earlier deterministic results of T. Kato [6] and are obtained by treating the equation in vorticity form and reducing the latter to a random nonlinear parabolic equation. The solution has maximal regularity in the spatial variables and is weakly continuous in Image removed. Image removed. with respect to the time variable. Furthermore, we obtain the pathwise continuous dependence of solutions with respect to the initial data. This is a joint work with Viorel Barbu (Romanian Academy, Iasi).