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

2018; Scientific Research Publishing; Volume: 09; Issue: 04 Linguagem: Inglês

10.4236/am.2018.94029

2152-7393

Enrique Fernández‐Cara, Irene Marín-Gayte,

Nonlinear Partial Differential Equations

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.