Stochastic Burgers Equation


Speaker: Sergei Kuksin (University of Paris 7)

Time: 2017.11.6  Stochastic Burgers Equation(I)

Time: 2017.11.8  Stochastic Burgers Equation(II)

Time: 2017.11.13  Stochastic Burgers Equation(III)

Time: 2017.11.15  Stochastic Burgers Equation(IV)

Time: 2017.11.20  Stochastic Burgers Equation(V)

Time: 2017.11.22  Stochastic Burgers Equation(VI)

Time: 2017.11.27  Stochastic Burgers Equation(VII)

Time: 2017.11.29  Stochastic Burgers Equation(VIII)

Place: N902

ABSTRACT. My course is dedicated to the stochastic Burgers equation under the periodic boundary conditions. This is a reach in properties nonlinear stochastic partial differential equation (SPDE) and a popular physical model. I will start with proving basic facts about the equation and defining the Markov process and the two Markov semigroups, related with it. This part of the course may be regarded as a brief introduction to SPDE. I will continue with more delicate qualitative properties of the equation, will use them to study the limits « time to infinity » and « viscosity to zero » and will explain the relevance of the two limits for physics. I will assume only very basic knowledge of the probability (random variables and their distribution,  independent random variables, elementary facts about the Wiener process), and of the PDE (Sobolev spaces of functions of one variable, basics about the heat and the Laplace equation).