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Navier-Stokes Solution Worth 1 Million Dollars
Posted Mon July 22, 2002 @10:09PM
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News The Clay Mathematics Institute of Cambridge, Massachusetts (CMI) has named seven “Millennium Prize Problems.” The Scientific Advisory Board of CMI selected these problems, focusing on important classic questions that have resisted solution over the years. The Board of Directors of CMI have designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each.

Among the seven problems is a call for the solution to the Navier-Stokes Equations. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.

In order to be awarded the prize, the solution must prove one of the four following statements:

  1. Existence and smoothness of Navier–Stokes solutions on R3
  2. Existence and smoothness of Navier–Stokes solutions in R3/Z3
  3. Breakdown of Navier–Stokes solutions on R3
  4. Breakdown of Navier–Stokes Solutions on R3/Z3

Since we don ’t even know whether these solutions exist our understanding is at a very primitive level. Standard methods from PDE appear inadequate to settle the problem. Instead we probably need some deep new ideas.

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