Question of the Week, 1.3.2011
Although first formulated in the 19th century, our knowledge of the Navier-Stokes equations remains minimal. These basic equations of fluid mechanics describe gas and liquid flow and can be derived by invoking conservation of momentum, mass, and energy for a continuum fluid. They form a set of nonlinear partial differential equations of second order, for which it has not been mathematically proved yet that smooth and global solutions always exist in three dimensions. Understanding the Navier-Stokes equations is also considered as a first step towards gaining better insight into the phenomenon of turbulence. In spite of the great importance for science and engineering, the Clay Mathematics Institute ranks this question among the seven most important open problems in mathematics and has offered a US-$ 1,000,000 prize for a solution or a counter-example.
Read more: http://www.claymath.org/millennium/Navier-Stokes_Equations/navierstokes.pdf
Thomas Jagau
