The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow
Bardos C, Titi ES, Wiedemann E (2012)
Publication Type: Journal article
Publication year: 2012
Journal
Book Volume: 350
Pages Range: 757-760
Journal Issue: 15-16
DOI: 10.1016/j.crma.2012.09.005
Abstract
We show that for a certain family of initial data, there exist non-unique weak solutions to the 3D incompressible Euler equations satisfying the weak energy inequality, whereas the weak limit of every sequence of Leray-Hopf weak solutions for the Navier-Stokes equations, with the same initial data, and as the viscosity tends to zero, is uniquely determined and equals the shear flow solution of the Euler equations corresponding to this initial data. This simple example suggests that, also in more general situations, the vanishing viscosity limit of the Navier-Stokes equations could serve as a uniqueness criterion for weak solutions of the Euler equations. © 2012.
Authors with CRIS profile
Involved external institutions
Université Sorbonne Paris Cité
France (FR)
University of California Irvine
United States (USA) (US)
University of British Columbia
Canada (CA)
France (FR)
University of California Irvine
United States (USA) (US)
University of British Columbia
Canada (CA)
How to cite
APA:
Bardos, C., Titi, E.S., & Wiedemann, E. (2012). The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow. Comptes Rendus Mathematique, 350(15-16), 757-760. https://dx.doi.org/10.1016/j.crma.2012.09.005
MLA:
Bardos, Claude, Edriss S. Titi, and Emil Wiedemann. "The vanishing viscosity as a selection principle for the Euler equations: The case of 3D shear flow." Comptes Rendus Mathematique 350.15-16 (2012): 757-760.
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