We investigate the creation and properties of eventual vacuum regions in weak solutions continuity equation, general, compressible Navier–Stokes equations, particular. The main results are based on analysis renormalized to pure transport equations their inter-relations which independent interest.

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed ‘Non-linear grid system’ is presented. The linear terms in Navier-Stokes equation are solved by CrankNicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Split...

We consider a splitting-based approximation of the abstract Riccati equation in the setting of Hilbert–Schmidt operators. The Riccati equation arises in many different areas and is important within the field of optimal control. While convergence of different methods for approximating the Riccati equation is discussed in several studies, none of them rigorously prove an order of convergence. In ...

This paper surveys various aspects of the hydrodynamic formulation of the nonlinear Schrödinger equation obtained via the Madelung transform in connexion to models of quantum hydrodynamics and to compressible fluids of the Korteweg type.

We have developed boundary integral equation formulas and a corresponding fast 3-D Stokes flow simulation program named FastStokes to accurately simulate viscous drag forces on geometrically complicated MEMS (microelectromechanical systems) devices. Unlike the 3-D finite element or finite difference solvers which often take days to run to completion or fail when geometry gets complicated, the F...