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Kazakhstani muslim scientist proves Navier-Stokes equations

Mukhtarbay Otelbayev, a professor at the Eurasian National University’s department of methods of mathematical simulation

Source : IINA / 01 Apr 2014

Mukhtarbay Otelbayev, a professor at the Eurasian National University’s department of methods of mathematical simulation, published a paper in the Mathematical Journal in which he proves the existence of a solution to an equation deemed one of the hardest in the world. The Navier Stokes Equation is One of seven Millennium Prize problems, which were set by the Clay Mathematics Institute in 2000.       

The equations are useful in academic and economic spheres as they may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing.

They describe the physics of many things, including the “lift” phenomenon of the modern airplane. The Navier–Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things.

Although the original equations were written down in the 19th century, our understanding of them has remained patched with no central proof the equations general principles. The challenge has been to make a substantial progress toward a mathematical theory, which will unlock the secrets hidden in the Navier-Stokes equations. The equations named after British and French Engineer Claude-Louis Navier– and Britain’s George Gabriel Stokes, are also of great interest in a purely mathematical sense which explains the amount of researchers within academic circles, numbering at around a thousand five-hundred.

The Clay Mathematical Institute, a UK non-profit organization based in Providence, Rhode Island, USA describes the equations as those that are believed to explain and predict fluid motion. The institute has called this one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize for a solution or a counter-example.

While confident in his findings and sure the academics in the West will have to agree, he says he does not want to spend the reward money on himself, saying the salary he currently earns suffices him and his wife. He says if the money is allowed to be kept by him, his wife will be ready to find use for it, whereas if she agrees, he would give the money to an orphanage.

"Over the years there have been several alleged solutions to the Navier-Stokes problem that turned out to be wrong," says Charles Fefferman of Princeton University, who wrote the official formulation of the problem for Clay. "Since I don't speak Russian and the paper is not yet translated, I'm afraid I can't say more right now."

However, Otelbayev is a professional, so mathematicians are paying more attention to his proof than is typical for amateur efforts to solve Millennium Prize problems, which are regularly posted online. Mukhtarbay Otelbayev who is currently is 71 has been working on this equation since 1979, is a doctor of physics and science at the Eurasian National University in Astana as well as director of Eurasian Mathematical Institute, Kazakhstan.

The Russian-speaking Misha Wolfson, a computer scientist and chemist at the Massachusetts Institute of Technology is attempting to spark an online, group effort to translate the paper. "While my grasp on the math is good enough to enable translation up to this point, I am not qualified to say anything about whether or not the solution is any good," he says.

Stephen Montgomery-Smith of the University of Missouri in Columbia, who is working with Russian colleagues to study the paper, is hopeful."What I have read so far does seem valid," he says "but I don't feel that I have yet got to the heart of the proof."

Otelbayev says that three colleagues in Kazakhstan and another in Russia agree that the proof is correct.

 

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