This paper is concerned with an optimal shape control problem for the stationary Navier–Stokes system. A two–dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By introducing an artificial compressibility term to relax the incompressibility constraints, we take the penalty method. T...

In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on important case no-slip boundary conditions, where it is now well established that collisions cannot occur finite time under certain assumptions. simplified framework, provide conditions which allow us to prove possible even absence topological contact. Our results lead con...

unsteady hydromagnetic generalised couette flow of a viscous, incompressible and electrically conducting fluid between two horizontal parallel porous plates darcian channel in the presence of a uniform transverse magnetic field taking hall current and ion-slip into account in a rotating system is investigated. an exact solution of the governing equations is obtained by laplace transform techniq...