Non-uniqueness for the Euler equations: The effect of the boundary

Bardos C, Szekelyhidi L, Wiedemann E (2014)

Publication Type: Journal article, Review article

Publication year: 2014

Journal

Russian Mathematical Surveys Institute of Physics: Pre-print only

Book Volume: 69

Pages Range: 189-207

Journal Issue: 2

DOI: 10.1070/RM2014v069n02ABEH004886

Abstract

Rotational initial data is considered for the two-dimensional incompressible Euler equations on an annulus. With use of the convex integration framework it is shown that there exist infinitely many admissible weak solutions (that is, with non-increasing energy) for such initial data. As a consequence, on bounded domains there exist admissible weak solutions which are not dissipative in the sense of Lions, as opposed to the case without physical boundaries. Moreover, it is shown that admissible solutions are dissipative if they are Hölder continuous near the boundary of the domain. © 2014 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

University of Paris 7 - Denis Diderot / Université Paris VII Denis Diderot FR France (FR) Universität Leipzig DE Germany (DE) University of British Columbia CA Canada (CA)

How to cite

APA:

Bardos, C., Szekelyhidi, L., & Wiedemann, E. (2014). Non-uniqueness for the Euler equations: The effect of the boundary. Russian Mathematical Surveys, 69(2), 189-207. https://dx.doi.org/10.1070/RM2014v069n02ABEH004886

MLA:

Bardos, C., L. Szekelyhidi, and Emil Wiedemann. "Non-uniqueness for the Euler equations: The effect of the boundary." Russian Mathematical Surveys 69.2 (2014): 189-207.

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