We discuss a basic iterative method by solving u and p alternatively. Starting from some initial guess u, p, one iteration going from (u, p) to (u, p) is (1) Fix p, solve for u; (2) Fix u, solve for p. When p is fixed, there are two equations for u. We can first solve the momentum equation to get u (the term B p is moved to the right hand side), i.e., Au = f −B p. But unless p is the exact solu...

The goal of this article is the study of the approximate controllability for two approximations of Navier Stokes equations with distributed controls. The method of proof combines a suitable lin-earization of the system with a xed point argument. We then are led to study the approximate controllability of linear Stokes systems with potentials. We study both the case where there is no constraint ...

We establish the vanishing viscosity limit of the Navier-Stokes equations to the isentropic Euler equations for one-dimensional compressible fluid flow. For the NavierStokes equations, there exist no natural invariant regions for the equations with the real physical viscosity term so that the uniform sup-norm of solutions with respect to the physical viscosity coefficient may not be directly co...

Compressible Navier–Stokes models for quantum fluids are reviewed. They are derived from a collisional Wigner equation by a moment method and a Chapman–Enskog expansion around the quantum equilibrium. Introducing a new velocity variable, the barotropic quantum Navier-Stokes model can be reformulated as a viscous quantum Euler system, which possesses a new Lyapunov (energy) functional. This func...

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian re...

The present work introduces a modified scheme for the solution of compressible 2-D full Navier-Stokes equations, using Flux Vector Splitting method. As a result of this modification, numerical diffusion is reduced. The computer code which is developed based on this algorithm can be used easily and accurately to analyze complex flow fields with discontinuity in properties, in cases such as shock...

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.

Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlevé equation is made explicit. It is shown that the monodromy identity, relating the topological monodromy and Stokes matrices, is useful for some quantum differentia...

This paper is concerned with the self-similar solutions to the compressible Navier-Stokes equations of a 1D viscous polytropic ideal gas. Our results show that there exist neither forward nor backward selfsimilar solutions with finite total energy, which generalizes the results for the case of the isothermal compressible Navier-Stokes equations in Z. Guo and S. Jiang (Self-similar solutions to ...