# Student Colloquium, Nikolaj Leonhard Daugaard Peters

*Supervisor: Jürgen Schmiegel *

Title: Navier Stokes: The Million Dollar Question

Fluid dynamics is governed by two central equations derived from the conservation of mass and momentum respectively, and while the former is quite nice to work with, the latter, known as the Navier-Stokes equation, has always been notoriously difficult to solve due to its nonlinearity. Physicists, engineers, and mathematicians have come and gone, but the problem of figuring out whether or not smooth solutions always exist has remained, and since the beginning of the 21st century it has even been given a bounty of one million dollars to whoever manages to figure out the answer.

Due to its analytic impracticality most of the students in the physics department have never even laid eyes on it despite living in a world quite literally filled to the brim with fluids. Therefore, I seek to introduce it in its most common form before loosely deriving why it looks the way it does. This will be followed by a classic problem; that being steady laminar flow through a pipe. The result of the calculation will be discussed before diving into the difficulties and results of the now century old problem giving way to the central question:

“Why is solving this problem still important?”