Navier-Stokes equations: Unpredictability even without butterflies?


Mathematically, the movement of a fluid is described with the so-called Navier-Stokes equations. In the spirit of Newtonian mechanics, these equations should determine the future motion of a fluid from its initial state. However, despite remarkable efforts in this direction over more than a century, this determinism has not yet been proved, or disproved, mathematically. This paper offers a general perspective on the Navier-Stokes equations, the fourth millennium problem.


Navier-Stokes equations; fluid mechanics; meteorology; Newtonian determinism; millennium problems


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Seregin, G., & Šverák, V. (2017). On global weak solutions to the Cauchy problem for the Navier-Stokes equations with large L3-initial data. Nonlinear Analysis, 154, 269–296. doi: 10.1016/

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