Navier-Stokes: one equation to rule them all

A leading Millennium Prize Problem is the Navier-Stokes equation, which, if solved, could model the flow of any fluid – that means how aeroplanes navigate the skies, how water meanders in a river and how the flow of blood courses through your blood vessels… Understanding these equations in more detail will lead to scientific advances in all of these fields: better aircraft design, improved flood defences, and better drug delivery in the body. Fluids expert and mathematician Keith Moffatt took me down to the deep dark depths of Cambridge’s maths lab…

  • For most fluids, including air and water, the Navier-Stokes equations are based on Newton’s Laws and were first written down in the 19th century
  • The millennium problem is to answer the question of whether or not the equations can become infinite
  • It cannot be solved with a computer because a computer programme will break down before the singularity at infinity is reached
  • A real-world example is when two tornado-like vortices collide and undergo a process called ‘vortex reconnection’

You can listen to the full interview for the Naked Scientists here.

And you can read more about the Navier-Stokes equations and all of the Millennium Problems here.

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