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arXiv · 1710.01579

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

Luigi C. Berselli·Simone Fagioli·Stefano Spirito
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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 theta-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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Luigi C. Berselli, Simone Fagioli, Stefano Spirito. 2017-10-04. Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization. https://doi.org/10.1016/j.matpur.2018.09.004

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