Navier-Stokes Equations Solved?

Have you seen this?

A news website in Kazakhstan ( is reporting that Mukhtarbai Otelbayev from the Eurasian National University has proved that the Navier Stokes equations have a strong unique solution.

If verified, Otelbayev has solved one of the Clay Mathematics Institute’s seven millennium problems. A prize of $1 million would be awarded for a solution.

A PDF of  Existence of a Strong Solution of the Navier Stokes Equations is available online but is written in Russian. However, there is an English language abstract at the end of the paper.

I first saw heard about this yesterday morning (12 Jan 2014) in a tweet from @SimScale.

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8 Responses to Navier-Stokes Equations Solved?

  1. Pingback: This Week in CFD | Another Fine Mesh

  2. Does the article shows THE solution for generic geometry and boundary conditions ir does it proves the EXISTENCE of a solution, that hasn’t been found yet?

  3. John Chawner says:

    The proof is one of existence and uniqueness.

  4. Solutions of Navier-Stokes Equations –
    The Navier-Stokes equations have been solved analytically by A. A. Frempong
    There is no need for proof of existence of solutions. See

    • John Chawner says:

      Hello A.A.

      Thanks for the pointer to your analytical solution of the N-S equations. If you have not done so already I urge you to submit your solution to the Clay Institute in order to capture the prize.

      • Many thanks, John.
        The solutions have been updated to include the solutions of the hitherto unsolved system of magnetohydrodynamic equations, with the new title “Solutions of Navier-Stokes Equations plus Solutions of Magnetohydrodynamic Equations. (at

  5. Pingback: This Week in CFD | Another Fine Mesh

  6. The Navier-Stokes equations have been solved, since about two years ago. Particularily, it shown that without gravity forces on earth, there would be no imcompressible fluid flow as is known. Also shown is why and when turbulence occurs in incompressible fluid flow. The solutions have been found to be very similar (except for the constants involved) to the motion and fluid pressure equations of elementary physics.

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