in this research, the effect of surface roughness and bubble injection on skin friction and hydrodynamic drag force has been numerically considered. this research is based on taylor-couette flow. considered flow includes two concentric cylinders which internal cylinder is movable and external is immovable. the effective equations on the flow includes: equations of momentum, continuous, turbulen...

In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated wit...

Adiscrete version of Lagrangian reduction is developed within the context of discrete time Lagrangian systems on G G, where G is a Lie group. We consider the case when the Lagrange function is invariantwith respect to the action ofan isotropysubgroup ofa¢xed element in the representation space of G. Within this context, the reduction of the discrete Euler^Lagrange equations is shown to lead to ...

This paper is concerned with the following Euler-Lagrange system \[ \begin{cases} \frac{d}{dt} \mathcal{L}_v(t,u(t),\dot{u}(t)) = \mathcal{L}_x(t,u(t),\dot{u}(t)) \quad \textrm{for a.e. $t \in [-T,T]$}, \\ u(-T) u(T), \mathcal{L}_v(-T,u(-T),\dot{u}(-T)) \mathcal{L}_v(T,u(T),\dot{u}(T)), \end{cases} \] where Lagrangian given by $\mathcal{L} F(t,x,v) + V(t,x) \langle f(t), x \rangle$, growth cond...

The basic aim is to extend some results and concepts of nonautonomous second order differential systems with convex potentials to the new context of multi-time Poisson-gradient PDE systems with convex potential. In this sense, we prove that minimizers of a suitable action functional are multiple periodical solutions of a Dirichlet problem associated to the Euler-Lagrange equations. Automaticall...

A surface of codimension higher than one embedded in an ambient space possesses a connection associated with the rotational freedom of its normal vector fields. We examine the Yang-Mills functional associated with this connection. The theory it defines differs from Yang-Mills theory in that it is a theory of surfaces. We focus, in particular, on the Euler-Lagrange equations describing this surf...