Interpreting convex integration results in hydrodynamics

Gregory Eyink; Heiko Gimperlein; Nigel Goldenfeld; Michael Grinfeld; Ilya Karlin; Robin J. Knops; Florian Kogelbauer; Ondřej Kreml; Colin McLarty; Simon Markfelder; Mikhail Osipov; Marshall Slemrod

doi:10.4171/mag/256

Interpreting convex integration results in hydrodynamics

Gregory Eyink, Heiko Gimperlein, Nigel Goldenfeld, Michael Grinfeld, Ilya Karlin, Robin J. Knops, Florian Kogelbauer, Ondřej Kreml, Colin McLarty, Simon Markfelder, Mikhail Osipov, Marshall Slemrod

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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.

Original language	English
Pages (from-to)	29-38
Number of pages	10
Journal	European Mathematical Society Magazine
Issue number	136
DOIs	https://doi.org/10.4171/mag/256
Publication status	Published - 8 Jul 2025

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title = "Interpreting convex integration results in hydrodynamics",

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.",

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AU - Eyink, Gregory

AU - Gimperlein, Heiko

AU - Goldenfeld, Nigel

AU - Grinfeld, Michael

AU - Karlin, Ilya

AU - Knops, Robin J.

AU - Kogelbauer, Florian

AU - Kreml, Ondřej

AU - McLarty, Colin

AU - Markfelder, Simon

AU - Osipov, Mikhail

AU - Slemrod, Marshall

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AB - 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.

U2 - 10.4171/mag/256

DO - 10.4171/mag/256

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SP - 29

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JO - European Mathematical Society Magazine

JF - European Mathematical Society Magazine

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ER -

Interpreting convex integration results in hydrodynamics

Abstract

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