Article citationsMore>>

Dean, E.J. and Glowinski, R. (1993) On Some Finite Element Methods for the Numerical Simulation for Incompressible Viscous Flow. Cambridge University Press, New York, 109-150.

has been cited by the following article:

• TITLE: A New Proof of the Existence of Suitable Weak Solutions and Other Remarks for the Navier-Stokes Equations

  AUTHORS: Enrique Fernández-Cara, Irene Marín-Gayte

  KEYWORDS: Navier-Stokes Equations, Regularity, Caffarelli-Kohn-Nirenberg Estimates, Semi-Implicit Euler Approximation Schemes

  JOURNAL NAME: Applied Mathematics, Vol.9 No.4, April 30, 2018

  ABSTRACT: We prove that the limits of the semi-discrete and the discrete semi-implicit Euler schemes for the 3D Navier-Stokes equations supplemented with Dirichlet boundary conditions are suitable in the sense of Scheffer [1]. This provides a new proof of the existence of suitable weak solutions, first established by Caffarelli, Kohn and Nirenberg [2]. Our results are similar to the main result in [3]. We also present some additional remarks and open questions on suitable solutions.