Navier-Stokes equations: Unpredictability even without butterflies?

Authors

  • Xavier Mora Autonomous University of Barcelona (Spain).

DOI:

https://doi.org/10.7203/metode.0.9415

Keywords:

equacions de Navier-Stokes, mecànica de fluids, meteorologia, determinisme newtonià, problemes del mil·lenni

Abstract

Mathematically, the motion of a fluid is described by the so-called Navier-Stokes equations. In the spirit of Newtonian mechanics, these equations should determine the future motion of the fluid out of its initial state. However, despite the significant effort made for more than a century, this determinism has not yet been mathematically proved nor disproved. This paper offers a general perspective on the Navier-Stokes equations, the fourth millennium problem.

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Author Biography

Xavier Mora, Autonomous University of Barcelona (Spain).

Associate professor of Applied Mathematics at the Department of Mathematics in the Autonomous University of Barcelona (Spain). He obtained his PhD in Mathematics at the same university in 1982 and he worked in the field of partial differential equations. Currently, he works in voting and election methods.

References

Mora, X. (2008). Les equacions de Navier-Stokes. Un repte al determinisme newtonià. Butlletí de la Societat Catalana de Matemàtiques, 23, 53–120. doi: 10.2436/20.2002.01.12

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/j.na.2016.01.018

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Published

2018-06-05

How to Cite

Mora, X. (2018). Navier-Stokes equations: Unpredictability even without butterflies?. Metode Science Studies Journal, (8), 43–49. https://doi.org/10.7203/metode.0.9415
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Issue

Making science: A multitude of perspectives (2018)

Section

The millennium problems. Challenges to further mathematics

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