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A new proof of the existence of suitable weak solutions and other remarks for the Navier-Stokes equations

 

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Opened Access A new proof of the existence of suitable weak solutions and other remarks for the Navier-Stokes equations
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Author: Fernández Cara, Enrique
Marín Gayte, Irene
Date: 2018-04
Published in: Applied Mathematics, 9 (4), 383-402.
Document type: Article
Abstract: We prove that the limits of the semi-discrete and the discrete semi-implicit Euler schemes for the 3D Navier-Stokes equations upplemented with Dirichlet boundary conditions are suitable in the sense of Scheffer. This provides a new proof of the existence of suitable weak solutions, first established by Caffarelli, Kohn and Nirenberg. Our results are similar to the main result in Guermond, J.-L. (2007) Faedo-Galerkin Weak Solutions of the Navier-Stokes Equations with Dirichlet Boundary Conditions Are Suitable. Journal de Mathématiques Pures et Appliquées, 88, 87-106. We also present some additional remarks and open questions on suitable solutions.
Size: 429.1Kb
Format: PDF

URI: https://hdl.handle.net/11441/86566

DOI: 10.4236/am.2018.94029

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