Three-Dimensional Navier-Stokes Equations for Turbulence

Luigi C. Berselli has been a full professor of Mathematical Analysis since 2015, and previously held positions of adjunct and associate professor, all at the Università di Pisa, Italy. He also has held visiting professorships at several institutions, including la Scuola Normale Superiore di Pisa, SISSA Trieste, the University of Rennes, and the University of Freiburg. Throughout his research career he has been very interested in both theoretical and applied analysis of PDEs, especially the initial-boundary value problems related to incompressible Newtonian and non-Newtonian fluids, with applications to turbulence, biomedical engineering, and geophysical flows. He is author of about 80 research papers in international journals and 1 monograph published in 2006. He has recently organized several conferences and is associate editor for 3 journals.

1. Introduction
2. On weak and strong solutions
3. Global energy conservation
4. Local energy inequality
5. Numerical construction of physically reasonable solutions
6. Long-time behavior of the energy