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.