Navier-Stokes-R Sir

 Okay, I am in awe of R Sir, have successfully cleared Advanced PDE after much stress (88 marks nonetheless, 2 short of the perfect A grade) and have gone to a PDE Workshop at CAM with a dubious level of utility extracted. Still, my heart yearns for more PDE and R Sir. Krantz's Partial Differential Equations and Complex Analysis sits proudly on my table and combines three of my favourite things in Mathematics. 

So when R Sir sent a mail announcing that he wants to lecture from Robinson et al's The Three-Dimensional Navier–Stokes Equations, I was perhaps one of the first to reply back to get on the mailing list. Timing is an issue this semester, but still, I can't bring myself to pass up this opportunity.  

He is lecturing in a very Feynman technique sort of way to a mixed audience of postdocs, PhDs, advanced undergraduates and even physicists! In his own words:

I am seeking an audience that is willing to hear me lecture on whatever I have managed to understand from the first four chapters of that book (I haven't attempted anything beyond that.......trying to understand the first four chapters is a sufficiently ambitious goal). 

My goal is to try to unravel the proof of the existence of a weak solution for the Navier-Stokes equation. 

If you are interested in listening to what I have figured out....

The thing is, I don't particularly care about the Navier-Stokes equation or Fluid Mechanics for that matter.  First, I am not that interested in physics myself. Second, despite the mythicalization and the omnipowerful status granted to the problem in online discourse due to the Millennium Prize, it fails to account for many things and doesn't even correctly model water at very small scales, which is not a criticism so much as a reminder of what the model is and what it is not ought to be evaluated to. Nor do I care much for the classical solutions, I am much more interested in Weak Solutions and the techniques of manipulating a nonlinear PDE. My point of view seems to be shared by R Sir too, for when talking of some boundary constraints inthe case of the Torus, he clearly stated:

Although I personally don't care about the Physics.

Literally my words. He then went out to start from the very start, the Geometer's definition of Laplacian:

$$ \Delta := -\left( \frac{\partial^2}{\partial x_1^2} + \frac{\partial^2}{\partial x_2^2} + \frac{\partial^2}{\partial x_3^2} \right) $$

 Not that PDE persons', not analysts', not physicists', but of his own tribe. No wonder we got assignment problems from Warner's Foundations of Differentiable Manifolds and Lie Groups in the first (mind you, first, not the Advanced course) PDE course. Like me, to him, PDE is a tool and a delightful one at that. I, too, have started to prefer his definition of Laplacian, it creates some notational inconsistencies between my thesis and the bibliography, but the results about Subharmonic functions make much more sense with this definition. 

I am sure a lot many people will drop starting today, but I aim to complete the lectures with perfect attendence. LB, with our firendship levels up on the sky, will also be attending so at the very least we will have fun tackling stuff we didn't understand. I can't wait till my COmprehencive exams after which I will be beyond the cycle of mid sems and end sems तस्य हि ध्रुवो मृत्युर्ध्रुवं जन्म मृतस्य च. Passing the comprehencive is the Nirvana moment of the PhD life. When one can just audit courses witjhout caring about exams. R Sir have just granted me this boon early, and I will make the most of it.