The understanding and description of turbulent flows poses several different problems in which theory, modeling, and (numerical) experiments interact in a multidisciplinary way. In this talk we present some of the basic tools, focusing on the mathematical foundation of the models used to describe the larger scales of the incompressible motions at high Reynolds number. Recent perspectives and open problems are also discussed.
Luigi C. Berselli earned his master in pure mathematics from the Scuola Normale Superiore (SNS) in 1995 and the PhD in Mathematics from the University of Pisa in 2000. He is full professor at the University of Pisa since 2016. He is an expert in the mathematical theory and modeling of PDEs' describing turbulent and non-Newtonian fluids. He also interacted with applied scientists to address problems in engineering, robotics, medical science, and volcanology. He is author of about 100 scientific papers and 2 books in the area of nonlinear PDEs.