Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation
Analysis of PDEs
2016-05-17 v1
Abstract
In this paper we consider the Navier-Stokes equations supplemented with either the Dirichlet or vorticity-based Navier boundary conditions. We prove that weak solutions obtained as limits of solutions to the Navier-Stokes-Voigt model satisfy the local energy inequality. Moreover, in the periodic setting we prove that if the parameters are chosen in an appropriate way, then we can construct suitable weak solutions trough a Fourier-Galerkin finite-dimensional approximation in the space variables.
Keywords
Cite
@article{arxiv.1605.04688,
title = {Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt Approximation},
author = {Luigi C. Berselli and Stefano Spirito},
journal= {arXiv preprint arXiv:1605.04688},
year = {2016}
}