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  2. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, NavierStokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...

  3. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_existence...

    The NavierStokes existence and smoothness problem concerns the mathematical properties of solutions to the NavierStokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the NavierStokes equations are used in many practical applications.

  4. Category:Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Category:Millennium_Prize...

    Pages in category "Millennium Prize Problems" The following 8 pages are in this category, out of 8 total. ... NavierStokes existence and smoothness; P.

  5. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    The numerical solution of the NavierStokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation or ...

  6. Nonlinear partial differential equation - Wikipedia

    en.wikipedia.org/wiki/Nonlinear_partial...

    For nonlinear equations these questions are in general very hard: for example, the hardest part of Yau's solution of the Calabi conjecture was the proof of existence for a Monge–Ampere equation. The open problem of existence (and smoothness) of solutions to the NavierStokes equations is one of the seven Millennium Prize problems in ...

  7. Template:Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Template:Millennium_Prize...

    Millennium Prize Problems; Birch and Swinnerton-Dyer conjecture; Hodge conjecture; NavierStokes existence and smoothness; P versus NP problem; Poincaré conjecture (solved) Riemann hypothesis; Yang–Mills existence and mass gap

  8. List of unsolved problems in physics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Under what conditions do smooth solutions exist for the NavierStokes equations, which are the equations that describe the flow of a viscous fluid? This problem, for an incompressible fluid in three dimensions, is also one of the Millennium Prize Problems in mathematics. [66]

  9. Stokes approximation and artificial time - Wikipedia

    en.wikipedia.org/wiki/Stokes_approximation_and...

    In the above equation stoke assume that at, non-stationary Navier Stokes problem converge towards the solution of the correspondent stationary problem. This solution will not depend upon the function . If this is used for the above equation consisting of Navier stokes equation and continuity equations with time derivative of pressure, then the ...