In this work, we study theoretically and numerically the equations of Stokes Navier-Stokes under power law slip boundary condition. We establish existence a unique solution by using monotone operators theory for whereas equations, construct means Galerkin's approximation combined with some compactness results. Next, formulate analyze finite element approximations associated to these problems. d...

In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...

We consider the three-dimensional incompressible Navier-Stokes equations in a domain of the form 0 (0;). We assume no-slip boundary conditions on @ 0 (0;), periodic conditions on 0 f0;g, and show that with certain assumptions on the initial condition and forcing function a strong solution exists for all time. Physically, these boundary conditions model uid ow in a pipe where the innow and outto...