In this study, a new computing model is developed using the strength of feed-forward neural networks with Levenberg–Marquardt scheme-based backpropagation technique (NN-BLMS). It used to find solution for nonlinear system obtained from governing equations magnetohydrodyanmic (MHD) boundary layer flow over stretching sheet. Moreover, partial differential (PDEs) MHD sheet are converting into ordi...

In this paper, we study the effect of MHD turbulence on the dynamics of dust particles in protoplanetary disks. We vary the size of the particles and relate the dust evolution to the turbulent velocity fluctuations. We performed numerical simulations using two Eulerian MHD codes, both based on finite difference techniques: ZEUS– 3D and NIRVANA. These were local shearing box simulations incorpor...

Boundary element methods are being applied with increasing frequency to time dependent problems, especially to boundary value problems for parabolic differential equations. Here we shall consider the heat equation as the prototype of such equations. Various types of integral equations arise when solving boundary value problems for the heat equation. An important one is the single layer heat pot...

Recently, observations from the Polar and Cluster satellites have indicated that largeamplitude kinetic Alfvén waves are observed throughout the plasma sheet, particularly at the plasma sheet boundary layers, during substorms. These waves may be directly produced by reconnection processes in the tail, or indirectly through linear or nonlinear mode conversion or by localized plasma flows in the ...

A steady three-dimensional Magnetohydrodynamic (MHD) boundary layer viscous flow and heat transfer due to a permeable stretching sheet with prescribed surface heat flux is studied in presence of a uniform applied magnetic field transverse to the flow. Using the implicit finite-difference scheme, known as the Keller-box method, the nonlinear ordinary differential equations are solved. The veloci...

In this paper, we obtain global small solutions and decay estimates for the two-dimensional MHD boundary layer in Gevrey space without any structural assumptions, generalizing results of [20] analytic space. The proof method is mainly inspired by [14] [26], using new auxiliary functions finer analysis to overcome difficulty loss derivatives then well-posedness 32

A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability are given. Moreover, it is shown that we can obtain ...

This manuscript is a survey on results related to boundary layers and the vanishing viscosity limit for incompressible flow. It is the lecture notes for a 10 hour minicourse given at the Morningside Center, Academia Sinica, Beijing, PRC from 11/28 to 12/07, 2007. The main topics covered are: a derivation of Prandtl’s boundary layer equation; an outline of the rigorous theory of Prandtl’s equati...