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.

Author Details

Luigi C. Berselli