Nonlinear Partial Differential Equations

Date: April 21, 2015

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Cecilia Mondaini, Texas A&M University

Title: Nonlinear PDEs Seminar

Abstract:

Title: Statistical solutions of general evolution equations

Abstract:

The theory of statistical solutions was initially developed for the treatment of the Navier-Stokes equations, a widely accepted model of turbulent flows, in order to understand some properties of such flows in a deep and rigorous way. In this talk, I would like to present a work on the extension of this theory to general evolution equations. The idea is to allow for a similar treatment to other evolution equations which, just like the Navier-Stokes equations, display the property of global existence of weak solutions without a known result of global uniqueness. I will focus on the abstract definitions of statistical solutions and on their existence for the corresponding initial-value problems. Some model examples will also be provided, illustrating the applicability of this abstract theory.