107 KAM Mathematical Colloquium

107 KAM Mathematical Colloquium

Vladimir Sverak

University of Minnesota

IS THE NAVIER--STOKES EQUATION COMPLETE AS A MATHEMATICAL MODEL?


Tuesday June 12, 2018, 14:00
room S3, 3rd floor
MFF UK, Malostranské nám. 25, Praha 1 

Abstract

The Navier--Stokes equation is a fundamental mathematical model of fluid motion. It is a Newtonian model, and one can ask if it is mathematically complete in the following sense: assuming no ``outside disturbances'', does a complete knowledge of the state of the model at a given time uniquely determine the behavior of the model for all future? The answer is not clear (at least for the most natural classes of solutions) and in the lecture, we will discuss recent results related to this topic. The well-known Clay Millennium Problem concerning the regularity of the Navier--Stokes equation is closely related to the uniqueness question, although it is not equivalent to it.


O přednášejícím

Vladimir Sverak studoval na MFF, jeho vedoucim byl D. Preiss a posleze skolitelem J. Necas. Byl vynikajicim studentem a velmi zahy se proslavil na MFF i mezinarodne v oblasti PDE a specialne ve vyzkumu Navierovych--Stokesovych rovnic. Za svou vedeckou praci ziskal mezinarodni oceneni: Evropska cena za matematiku mu byla udelena na prvnim Evropskem kongresu matematiku v roce 1992 v Parizi (pripomenme, ze tuto cenu ziskal z ceskych matematiku pouze J. Matousek v roce 1996 a A. Naor v roce 2008). V. Sverak byl hostem prednich mezinarodnich instituci pred tim, nez se stal radnym profesorem a posleze cestnym McKnight profesorem na University of Minesota (od roku 2000). Vedecka cinnost V. Sveraka ziskala radu dalsich oceneni, z nichz jmenujme pouze prednasku na Mezinarodnim kongresu matematiku v r. 1994 v Curychu, prednasku na Evropskem kongresu matematiku v r. 2012 v Krakove a rovnez cenu Neuron v r. 2017. V. Sverak patri ke svetove nejznamejsim ceskym matematikum. Jeho prazske kolokvium je venovano hlavni oblasti jeho zajmu.