We study magnetohydrodynamic equations for a viscous incompressible resistive fluid in a thin 3D domain. We prove the global existence and uniqueness of solutions corresponding to a large set of initial data from Sobolev type space of the order 1/2 and forcing terms from L2 type space. We also show that the solutions constructed become smoother for positive time and prove the global existence o...

In this paper we examine two problems in steady incompressible viscous flow with a view to generating high-order perturbation solutions as regular expansions in powers of the Reynolds number. Thus, computer-algebra techniques are used to study the motions produced (a) by a Landau momentum source placed at the centre of a fluid-filled spherical shell, and (b) by a rotating sphere in both unbound...

We consider the free fall of a sphere above a wall in a viscous incompressible fluid. Weinvestigate the influence of boundary conditions on the finite-time occurrence of contactbetween the sphere and the wall. We prove that slip boundary conditions enable tocircumvent the ”no-collision” paradox associated with no-slip boundary conditions. Wealso examine the case of mixed bou...

Following Eggers and Dupont (1994), we will derive approximate equations of motion valid in the limit of slender jets i.e. jets for which the radial dimensions are much smaller than the longitudinal dimensions. We start by writing the full equations of motion for an incompressible viscous fluid in cylindrical (axisymmetric) coordinates. The equations for the two components of momentum can be wr...

Hydromagnetic flow and mass transfer of a viscous incompressible fluid over a microcantilever sensor surface are studied in the presence of slip flow. In addition, chemical reaction at the sensor surface is taken into account. The governing equations for the flow are reduced to a local nonsimilarity form. Resulting equations are solved numerically for various values of flow parameters. Effects ...

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...

The results of an experimental study the effects noises on flows in a rotating spherical layer are presented. Noise is introduced into flow form random fluctuations inner sphere rotational rate relative to time constant mean value. velocity was measured with laser Doppler anemometer. It found that equal amplitude, but different spectra cause generation intensity. shown increase average velociti...

We consider the controllability of a viscous incompressible fluid modeled by Navier–Stokes system with nonlinear viscosity. To prove to trajectories, we linearize around trajectory and corresponding linear includes nonlocal spatial term. Our main result is Carleman estimate for adjoint this system. This yields in standard way null local trajectories. method obtain completely general can be adap...