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Neustupa, J. and Penel, P. (1999) Regularity of a Suitable Weak Solution to the Navier-Stokes Equations as a Consequence of Regularity of One Velocity Component. In: Applied Nonlinear Analysis, Kluwer/Plenum, New York, 391-402.

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.