The age old problem of Navier- Stoke’s Equations and Von Neumann Machines!


Millennium Problems : These are very big deal when it comes to Mathematics. But, for some obscure reason, One of them is not very popular among Engineers, even though one of the last standing problems in classical physics – Navier–Stokes existence and smoothness (one of the millennium problems) is of major consequence to Fluid Dynamicists, Aerospace/Mechanical/Chemical Engineers and Many others alike. I still don’t know why is that the case. Maybe the recruiting agents at undergraduate level do not want to scare away students who are already bog down by assignments and homework based on the ‘Solved’ mysteries of last century. I agree, even ‘Euler’ equations – simplified form of N-V equations, will require a significant amount mathematical prowess to tame that beast ‘Computationally’ (leave aside analytically) …

Something interesting happened in February this year, Dr.Terence Tao from UCLA, has a new paper out. (Title Reads : Finite Time Blowup for an Averaged Three-Dimensional Navier-Stokes Equation). His new idea is making quite a buzz around but as most of them say, it just a new direction to the approach, but no way closer to resolving the problem. Next stop is to study the consequences of this paper and ( the one involving finite time blowup of Euler Equations), but that would be a summer Project altogether. I would be seeking help from some colleagues who have a formal training in Logic Gates. Next are the Von Neumann Machines. Still this cross pollination of different ideas from distant branches of Engineering might just pay off for the next generation wave of researchers … Yes it is as weird as Indian Hip Hop – Beware the MC !

Blowup :

Now, just to learn what it means to ‘Blow up’ a solution, We would need a whole lot of machinery of Numerical Methods and Linear Algebra. But in short means exactly what it sounds – Reaching non physical values of Physical entities ( or just infinities). Let the melody ring in your ear over and over again …

Computational Vs Theoretical Vs Experiments !!!!

This is how it feels sometimes:

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