Bio: Professor Vladimir Sverak obtained his doctorate under Jindřich Nečas at the Charles University in Prague in 1986. His postdoctoral stays were in Edinburgh (with John Ball) and in Bonn (with Stefan Hildebrandt). He has been a Professor at the University of Minnesota since 1994. Sverak studies partial differential equations. 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.

Title: Two spectral calculations and their applications to PDE analysis of incompressible fluid flows

Abstract: We will discuss two problems for the incompressible Navier-Stokes equations whose solutions can be obtained via computations of suitable spectra. The first concerns the uniqueness of the Leray-Hopf solutions, where an important spectral computation still needs computer assistance. The second concerns the long-distance behavior of the steady 3d solutions in exterior domains. Here the relevant spectral computations can be done by the traditional 'paper and pencil' methods and one can obtain certain higher-order asymptotics for the solutions that may be somewhat unexpected. The talk is based on joint works with Hao Jia and Julien Guillod.