DMS Stochastic Analysis Seminar

Time: Mar 22, 2023 (01:10 PM)
Location: 352 Parker Hall


Speaker: Cheuk-Yin Lee, National Tsing Hua University, Taiwan

Title: Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Abstract: In this talk, I will present my joint work with David Candil and Le Chen about nonlinear parabolic SPDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish explicit bounds for the moments and correlation function of the solutions under a rough initial condition that is given by a locally finite signed measure. Our focus is on studying how the >moment bounds and related properties of the solutions depend on the rough initial data and the smoothness and geometric property of the domain. For $C^{1,{\em a}}$-domains with Dirichlet boundary condition, we obtain moment bounds under a weak integrability condition for the initial data which need not be a finite measure. Our results also imply intermittency properties of the solutions.