Abstract. Fluid flows have always been important and interesting for people and there are several well-known problems associated with the basic equations describing them, the Navier-Stokes equations. Some of the problems have precise mathematical formulation (such as the regularity problem), some of them have a broader nature (such as the problem of turbulence), some of them are related to large-scale computing, and there are still other aspects. I will discuss some of these topics, focusing mostly on the PDE analysis angle.

Bio. V. Sverak studies partial differential equations. He obtained his doctorate with Jindřich Nečas at Charles University in Prague in 1986. His postdoctoral stays were in Edinburg (with John Ball) and in Bonn (with Stefan Hildebrandt). He has been a Professor at the University of Minnesota since 1994. He received an ECM prize at the first European Congress of Mathematicians in 1992. He has been a Distinguished McKnight University Professor at the University of Minnesota since 2000. In 2017 he received an award in mathematics from the Neuron Foundation in Prague.