Weak Solutions Constructed by Semi-Discretization are Suitable: The Case of Slip Boundary Conditions
Year: 2018
Author: Luigi C. Berselli
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 479–491
Abstract
We consider the initial boundary value problem for the three dimensional Navier-Stokes equations with Navier-type slip boundary conditions. After having properly formulated the problem, we prove that weak solutions constructed by approximating the time-derivative by backward finite differences (with Euler schemes) are suitable. The main novelty is the proof of the local energy inequality in the case of a weak solution constructed by time discretization. Moreover, the problem is analyzed with boundary conditions which are of particular interest in view of applications to turbulent flows.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2018-IJNAM-12526
International Journal of Numerical Analysis and Modeling, Vol. 15 (2018), Iss. 4-5 : pp. 479–491
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Navier-Stokes equations Euler scheme local energy inequality slip boundary conditions.