Three-Dimensional Incompressible Navier-Stokes Equations: Recent results on the local regularity of weak solutions

<p>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!</p> <p>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 <em> good</em> model?) also involves such mechanisms or whether it admits solutions with singularities?</p>