3 ms·
oh, this might help "Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and phys
by seles 16y ago
oh, this might help
"Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these 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."
http://www.claymath.org/millennium/Navier-Stokes_Equations/ http://www.claymath.org/millennium/Navier-Stokes_Equations/
- exit 16y agothat doesn't seem to setup an assertion for which a counter-example could be shown.
- thurn 16y agoMy understanding is that the Navier-Stokes problem has to do with showing that smooth solutions always exist for the three dimensional system of equations, so a counter-example would be a set of initial conditions for which no smooth solution exists. On Wikipedia, the problem is described as: "Prove or give a counter-example of the following statement: In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations." http://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness http://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smo...