Weak Solutions and Optimal Control of Hemivariational Evolutionary Navier-Stokes Equations under Rauch Condition. (14th October 2020)

• Record Type: Journal Article
• Authors: Mahdioui, Hicham; Ben Aadi, Sultana; Akhlil, Khalid
• Other Names: Ru Yuanfang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-10-14
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/6573219
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In this paper, we consider the 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 the Rauch condition, we use the Galerkin approximation method and a weak precompactness criterion 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. At 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.