A Calculation of Geodesics in Flat Robertson-Walker Space and its Folding
Our aim in the present article is to introduce and study new types of retractions of flat Robertson-Walker space. Types of the deformation retracts of flat Robertson-Walker space are presented. The relations between the folding and the deformation retract of flat Robertson-Walker space are deduced .Types of minimal retractions of flat Robertson-Walker space are also presented. Also, the isometric and topological folding in each case and the relation between the deformation retracts after and before folding have been obtained. The connection between isocurvature folding and tangent spaces are obtained. New types of homotopy maps are deduced
In this paper, we consider the density-dependent incompressible Navier–Stokes equations in with linearly growing initial velocity at infinity. We obtain a blow-up criterion and global well-posedness of the two-dimensional system. It generalized the local well-posedness results due to the recent work by the first and third authors to the global well-posedness in . Copyright © 2012 John Wiley & Sons, Ltd.