02/07/2001, 11:00 — 12:00 — Room P3.10, Mathematics Building
Patrick Penel, Université de Toulon-Var
Three-Dimensional Incompressible Navier-Stokes Equations: Recent
results on the local regularity of weak solutions
The Navier-Stokes equations are known since the 19th century.
They were derived under the assumption that the fluid is a
continuous medium, under Newton's law, and moreover under an a
priori assumption that velocity and pressure have a certain
smoothness. The existence of solutions with this smoothness in a
3D-case still remains an open mathematical problem!
Comment: There exist mechanisms in real fluids which do not
enable the speed of motion to increase above all limits. It is
highly desirable to know whether the Navier-Stokes model (a
good model?) also involves such mechanisms or whether it
admits solutions with singularities?
