Minimax Theory and its Applications 03 (2018), No. 1, 107--130
Copyright Heldermann Verlag 2018
Evolution Hemivariational Inequalities for Non-stationary Navier-Stokes Equations: Existence of Periodic Solutions by an Equilibrium Problem Approach
S. Ben Aadi
Department of Mathematics, Ibn Zohr University, Agadir, Morocco
Ouayl Chadli
Laboratoire d'Analyse Mathématiques et Applications, Ibn Zohr University, Agadir, Morocco
o.chadli@uiz.ac.ma
A. Koukkous
Laboratoire d'Analyse Mathématiques et Applications, Ibn Zohr University, Agadir, Morocco
a.koukkous@uiz.ac.ma
The main goal of this paper is to study the existence of solutions for non-stationary Navier-Stokes equations with a subdifferential boundary condition described by a superpotential function which is locally Lipschitz. The approach adopted in this paper is based on recent developments in the theory of equilibrium problems.
Keywords: Navier-Stokes equations, hemivariational inequalities, pseudomonotone operators, equilibrium problems, maximal bifunctions, pseudomonotone bifunctions, mollification.
MSC: 49J40, 47J20, 90C33, 65K10, 49M20
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