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

Research output: Contribution to journal › Article › peer-review

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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

PY - 2025/7/8

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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

EP - 38

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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