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The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré conjecture at the ...
This term makes the Navier–Stokes equations highly sensitive to initial conditions, and it is the main reason why the Millennium Prize conjectures are so challenging. In addition to the mathematical challenges of solving the Navier–Stokes equations, there are also many practical challenges in applying these equations to real-world situations.
Pages in category "Millennium Prize Problems" The following 8 pages are in this category, out of 8 total. ... Navier–Stokes existence and smoothness; P.
Navier–Stokes existence and smoothness; ... The conjecture was chosen as one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, ...
The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...
Millennium Prize Problems: Clay Mathematics Institute: Solution to any of the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap. United States: Monroe H. Martin Prize: University of Maryland ...
Under what conditions do smooth solutions exist for the Navier–Stokes 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. [70]
Prizes are often awarded for the solution to a long-standing problem, and some lists of unsolved problems, such as the Millennium Prize Problems, receive considerable attention. This list is a composite of notable unsolved problems mentioned in previously published lists, including but not limited to lists considered authoritative, and the ...