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.
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.