Recent Developments in the Navier-Stokes Problem

The Navier-Stokes equations: fascinating, fundamentally important, and challenging, . Although many questions remain open, progress has been made in recent years. The regularity criterion of Caffarelli, Kohn, and Nirenberg led to many new results on existence and non-existence of solutions, and the very active search for mild solutions in the 1990's culminated in the theorem of Koch and Tataru that, in some ways, provides a definitive answer.