13/03/2013, 16:30 — 17:30 — Sala P3.10, Pavilhão de Matemática
Werner Varnhorn, Kassel University, Germany
The Navier–Stokes Equations: A never ending challenge?
More than 2500 years after the famous statement πάντα
ῥεῖ by Heracleitos the investigation of the mechanical and
dynamical behavior of fluid flow is more than ever of fundamental
importance. Due to a large number of technical, experimental and
computational innovations and related theoretical problems the
investigation of fluid flow represents a challenging and exciting
subject requiring a wide variety of profound mathematical methods,
efficient numerical algorithms and complex experimental
simulations. Fascinating from the mathematical point of view, of
course, is the fact that the fundamental equations of
Navier–Stokes, formulated the first time by the French engineer
Navier in 1822, could not be solved in the general
three–dimensional case up to now. So the famous American Clay
Mathematics Institute created the Navier–Stokes Millennium Price
Problem and offered one Million US–Dollar for its solution,
stating: „Although the Navier–Stokes equations were written
down in the 19th Century, our understanding of them remains
minimal. The challenge is to make substantial progress toward a
mathematical theory, which will unlock the secrets hidden in the
Navier–Stokes equations“.
The lecture introduces the Navier–Stokes equations from an
historical and physical point of view, touches some fundamental
mathematical problems of viscous incompressible fluid flow and ends
up with new regularity results.
