Abstract. For many decades mathematicians have investigated the extra conditions that a Leray-Hopf solution must satisfy, in the three-dimensional case, in order to obey certain fundamental properties, such as validity of the energy equation, uniqueness and regularity. A typical example is the so called Prodi-Serrin-Ladyzhenskaya condition. Objective of this talk is to show that Leray-Hopf solutions are, indeed, not so special. More precisely, we prove that any distributional solution with initial data having finite energy that obeys the same extra conditions possesses, in fact, all the above mentioned properties.

Bio. Giovanni P. Galdi is Distinguished Research Professor of Mechanical Engineering and Materials Science, the Leighton E. and Mary N. Orr Professor of Engineering, and Professor of Mathematics at the University of Pittsburgh. Before joined University of Pittsburgh, he was a professor at the University of Ferrara (Italy), where he founded the School of Engineering in 1989. Prof. Galdi has made important contributions in various aspects of mathematical theory of fluid mechanics. Prof. Galdi has (co)authored over 170 peer-reviewed journal articles, and 9 books, and (co)edited 18 books, mostly dedicated to fluid mechanics. He is currently a member of the Editorial Board of several scientific Journals, including European Journal of Mechanics B/Fluids, and Nonlinear Analysis. He is also co-founder and Editor in Chief of the Journal of Mathematical Fluid Mechanics. Prof. Galdi is the three-time recipient of the Mercator Award from German Research Foundation in the years 2003, 2009 and 2014 for his “outstanding contributions to Mathematical Fluid Mechanics”.