Interpreting convex integration results in hydrodynamics

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Eyink, Gregory and Gimperlein, Heiko and Goldenfeld, Nigel and Grinfeld, Michael and Karlin, Ilya and Knops, Robin J. and Kogelbauer, Florian and Kreml, Ondřej and McLarty, Colin and Markfelder, Simon and Osipov, Mikhail and Slemrod, Marshall (2025) Interpreting convex integration results in hydrodynamics. European Mathematical Society Magazine, 136. pp. 29-38. ISSN 2747-7908 (https://doi.org/10.4171/mag/256)

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Abstract

The aim of this article is to encourage debate of issues of the applications of modern methods of mathematical analysis in fluid dynamics. A recent surprising result derived by convex integration techniques shows non-uniqueness of weak solutions in initial value problems of the Navier–Stokes equations. The question of relevance of such a result to physical observed flows allows a variety of answers, some of which are discussed below.

ORCID iDs

Eyink, Gregory, Gimperlein, Heiko, Goldenfeld, Nigel, Grinfeld, Michael ORCID logoORCID: https://orcid.org/0000-0002-3897-8819, Karlin, Ilya, Knops, Robin J., Kogelbauer, Florian, Kreml, Ondřej, McLarty, Colin, Markfelder, Simon, Osipov, Mikhail ORCID logoORCID: https://orcid.org/0000-0002-1836-1854 and Slemrod, Marshall;
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