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Young Measures Generated by Ideal Incompressible Fluid Flows

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Abstract

In their seminal paper, DiPerna and Majda (Commun Math Phys 108(4):667–689, 1987) introduced the notion of a measure-valued solution for the incompressible Euler equations in order to capture complex phenomena present in limits of approximate solutions, such as persistence of oscillation and development of concentrations. Furthermore, they gave several explicit examples exhibiting such phenomena. In this paper we show that any measure-valued solution can be generated by a sequence of exact weak solutions. In particular this gives rise to a very large, arguably too large, set of weak solutions of the incompressible Euler equations.

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  1. Mathematisches Institut, Universität Leipzig, Leipzig, Germany

    László Székelyhidi Jr. & Emil Wiedemann

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  1. László Székelyhidi Jr.
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  2. Emil Wiedemann
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Correspondence to László Székelyhidi Jr..

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Communicated by V. Šverák

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Székelyhidi, L., Wiedemann, E. Young Measures Generated by Ideal Incompressible Fluid Flows. Arch Rational Mech Anal 206, 333–366 (2012). https://doi.org/10.1007/s00205-012-0540-5

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