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Author: Admin | 2025-04-28
The Navier-Stokes existence and smoothness equation is at the heart of fluid dynamics. This means that they describe how fluids, along with fluid-like substances such as air, move through space.The Navier-Stokes existence and smoothness equation was developed in 1822 by Claude-Louis Navier and George Gabriel Stokes. This equation appears on the Clay Mathematics Institute’s list of Millenial Prize Problems that will pay out $1,000,000 to whoever solves it.The official statement they would have proved or disproved is as follows:In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.Clay Mathematics InstituteDifficulty Rating10/10This is one of the most important problems in physics that has plagued the mathematics and scientific community since its inception. In order to solve this problem, one would need a deep understanding of advanced Calculus, but more specifically, differential equations. However, some have speculated that a solution would be physically impossible.Real-World ApplicationsThe Navier-Stokes existence and smoothness equation has applications in fluid mechanics, aerodynamics, and in the engineering of aircraft. A proper solution would be revolutionary in the aerospace industry.If you’d like to learn about the other Millenial Prize Problems, you can check them out here:Wikipedia: Millenial Prize ProblemsMore Unsolved Math ProblemsIf you’re interested to learn more about the hardest unsolved math problems in the world, Wikipedia has a list of 100+ problems. The list is organized by the different branches of mathematics such as algebra and number theory. You can check out the list here:Wikipedia: List of unsolved problems in mathematicsRelated Articles
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