Weak solutions and optimal control of hemivariational evolutionary Navier-Stokes equations under Rauch condition
Analysis of PDEs
2020-10-29 v2
Abstract
In this paper we consider evolutionary Navier-Stokes equations subject to the nonslip boundary condition together with a Clarke subdifferential relation between the dynamic pressure and the normal component of the velocity. Under Rauch condition, we use the Galerkin approximation method and a weak precompactness criteria to ensure the convergence to a desired solution. Moreover a control problem associated with such system of equations is studied with the help of a stability result with respect to the external forces. In the end of this paper, a more general condition due to Z. Naniewicz, namely the directional growth condition, is considered and all the results are reexamined.
Keywords
Cite
@article{arxiv.2007.10846,
title = {Weak solutions and optimal control of hemivariational evolutionary Navier-Stokes equations under Rauch condition},
author = {Hicham Mahdioui and Sultana Ben Aadi and Khalid Akhlil},
journal= {arXiv preprint arXiv:2007.10846},
year = {2020}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:2001.09449