Mathematical Physics

    

Singularities in 3D: the Mathematical Challenge of Euler and Navier-Stokes

Authors: Diego Cordoba Gazolaz, Luis Martinez Zoroa, Abdelmajid Ben Hadj Salem

The Euler and Navier-Stokes equations describe the motion of fluids, but it is still unknown whether their smooth solutions (with $C^{infty}$ regularity) can develop singularities in finite time.This enigma, one of the «Millennium Prize Problems», poses fundamental mathematical and physical challenges. In this article, we review what singularities are, the main mechanisms proposed for their formation (selfsimilar solutions and vorticity cascades) as well as recent advances that shed new light on this problem in three dimensions.

Comments: 19 Pages. In French, the article was translated from spanish.

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Submission history

[v1] 2026-02-08 17:19:27

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