The Butterfly Effect

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Clay Mathematics Institute Millenium Million-Dollar Prize Problems • Birch and Swinnerton-Dyer Conjecture • Hodge Conjecture • Navier-Stokes Equations • P vs NP • Poincaré Conjecture • Riemann Hypothesis • Yang-Mills <strong>The</strong>ory
Navier-Stokes Equations For smooth initial conditions and suitably regular boundary conditions do there exist smooth, solutions at all future times?
Page 1 and 2: The Butterfly Effect: Myth or Reali
Page 3 and 4: dX dt dY dt dZ dt =− σX + σY =
Page 5 and 6: “The following is the text of a t
Page 7 and 8: “It is proposed that certain form
Page 9 and 10: −5/3 2/3 If Ek ( ) k then τ −
Page 11 and 12: Ek ( ) : 3 k − Ek ( ) : 5/3 k −
Page 13: Clay Mathematics Institute Milleniu
Page 17 and 18: Climate Change is the “defining i
Page 19 and 20: Standard Paradigm for a Weather/ Cl
Page 21 and 22: 80-km resolution
Page 23 and 24: The “Real Butterfly Effect” rai

The Butterfly Effect

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