We prove that weak solutions obtained as limits of certain numerical space–time discretizations are suitable in the sense of Scheffer and Caffarelli–Kohn–Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the θ-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality.

Suitable weak solutions of the Navier–Stokes equations constructed by a space–time numerical discretization

Fagioli, Simone;Spirito, Stefano
2019-01-01

Abstract

We prove that weak solutions obtained as limits of certain numerical space–time discretizations are suitable in the sense of Scheffer and Caffarelli–Kohn–Nirenberg. More precisely, in the space-periodic setting, we consider a full discretization in which the θ-method is used to discretize the time variable, while in the space variables we consider appropriate families of finite elements. The main result is the validity of the so-called local energy inequality.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/130808
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