arXiv subjects
Publications and source records attributed to Hicham Mahdioui.
In this paper, we introduce the g-Bénard equations with time-fractional derivative of order $α\in (0, 1)$ in domains of $\mathbb R^2$. This equations model, the memory-dependent heat conduction of liquids in fractal media considered in g-framework. We aim to study the existence and uniqueness of weak solutions by means of standard techniques from Navier-Stokes equations theory and fractional calculus theory.
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.
In this paper we study existence, dependence and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier-Stokes equations but without making use of the theory of pseudo-monotone operators. To do so, we consider a classical assumption, due to J. Rauch, which constrains us to make a slight change on the definition of a solution. The Rauch assumption,, although insure the existence of a solution, does not allow the conclusion that the non-convex functional is locally Lipschitz. Moreover, two dependence results are proved, one with respect to changes of the boundary condition and the other with respect to the density of external forces. The later one will be used to prove the existence of an optimal control to the distributed parameter optimal control problem where the control is represented by the external forces.