Announcing an exact solution to the 3D Navier-Stokes Equation

Erica Grace Cabanilla, my ERDT administrator, who took charge of all my stipends, reminded me gently that I am supposed to give my exit report on Jan. 26 as Visiting Researcher, although my appointment letter from the Diliman Chancellor said Visiting Professor for one year at the College of Engineering. What is ERDT? I never really found out, but it has something to do with engineering, research and development. My tasks included supervising three research students on my quantum theory of turbulence. There were unaccomplished promises, but little did anyone suspect that at the end of the appointment, I was to offer the first exact solution to a 200-year-old problem in my planned exit report. ERDT and DOST are probably getting more than they bargained for, except that nobody seems to realize it, something to do with blissful ignorance. 

As you can see, there is a lot of ambiguity in my introductory paragraph, such is our country. But I had a good year at the Chemical Engineering Department of UP. My visits were intermittent as I shuttled between Columbia University, Harvard University, and UP. I may have even recovered all my travel expenses, ultimately, from the monthly stipends that I received. The foreign visitors sometimes get their entire sum for the year, but as I am a native, I was treated differently. So it was fun with all the hospitality. My favorite workplaces were the Starbucks Coffee at Katipunan Road, where I got to know the young mothers who dressed up their children to attend Miriam College — that reminded me of my days as stage father to a young ballerina, Marie, who danced with the Nutcracker Suite in New York, and Cordillera Café at the Vargas Museum, now closed.

Why this kind of introduction to a talk? Because I wish to teach students that research is a life, not just a dreamy chore. I learned about the Navier-Stokes Equation as a junior student in physics, self-taught, really from old editions of the English textbooks at the Main Library. I had a good classical education as a result, there was only one influential teacher in physics, Franco Mendiola, who gave up an early career in physics to become a Franciscan monk. No luck with apple trees in Marikina, I learned vector analysis under a camachile tree — it is still there. 

The Navier-Stokes equation (NSE) rules all of fluid dynamics, including, it was supposed to be, turbulence. Fluid dynamics, aerodynamics and turbulence were supposed to be together always. Except now, I know that NSE cannot explain turbulence, for I have given a negative proof of its inapplicability, that is why no one has explained the origin of turbulence for 200 years. This despite thousands of engineers, scientists, and mathematicians, and untold sums of money in search of turbulence. Why has everyone failed? Two reasons: (1) no one ever defined turbulence properly, and (2) people ignored atoms and molecules, discovered after the Navier-Stokes equation was formulated as a continuum, before Dalton proposed the existence of atoms and molecules. I see chemists and chemical engineers rolling with laughter. But really NSE is complicated enough without chemistry, that’s the story. Why am I so friendly with chemists and engineers? Because I started out as a chemical engineering student, seduced very quickly by physics.

But if molecules are that important, what is next? Quantum mechanics! Since very few engineers learned the subject, no engineer could be expected to use quantum mechanics to solve the riddle of turbulence. So in the end, my classical physics background: self-taught fluid mechanics, quantum mechanics, quantum kinetic equations, mathematics — some self-invented — and sheer conviction, allowed me to produce an exact solution to the problem of the Navier-Stokes equation. In addition, I used symbolic computation to display analytic and graphical results, all satisfying the Clay Institute of Mathematics Millennium Problem Definition for the Navier-Stokes Equation. It was not a frontal attack.

My solution sprung from an unheralded paper I wrote in 1997 at the Institute for Advanced Study in Princeton. Thirteen years later, I finally used it to solve an old problem. I rescued it from obscurity. But that is not uncommon: Oppenheimer waited 10 years to get his work on neutron stars recognized, Chandrasekhar waited 50 years before he got a Nobel on his work with white dwarfs. Both works used quantum mechanics. And now, Schroedinger’s quantum entanglement, after 80 years, is finding application in teleportation and cryptography. So what is a wait of 13 years?

So on Jan. 26, I will tell students about my now gnarled camachile tree, witness to my mathematical studies, which has always reminded me of my baffling year as an undergraduate with Prof. C. S. Lin who attempted to teach me what used to be known as advanced calculus. Then I asked why I got a humbling grade of 3, to which he replied, “but you were the only one who passed!” Prof. Lin, wherever you might be, I am happy to tell you that I am writing my first mathematics paper for the Bulletin of the American Mathematical Society to satisfy the requirement of the Clay Institute of Mathematics. I am also writing my first philosophy paper for the British Journal for the Philosophy of Science with the title “How do you solve a problem that you cannot define?” Yes, nobody has ever defined turbulence mathematically until a PBFM (poor boy from Marikina) proposed a precise definition.

It is a long way indeed from my camachile tree to the Department of Philosophy at Harvard University where I am certainly the oldest Fellow. In philosophy, I was told by a professor, the older you are the more respect you get! Very Asian, but almost un-American. So there, young kids, see you at the College of Engineering!

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Amador Muriel, a corresponding member of the National Academy of Science and Technology, may be reached at [email protected]. He has published “Quantum Nature of Turbulence” and now writes “Quantum Theory of Turbulence” at Harvard.