Approximation of a Class of Incompressible Third Grade Fluids Equations

Euler Equations of Incompressible Ideal Fluids

This article is a survey concerning the state-of-the-art mathematical theory of the Euler equations of incompressible homogenous ideal fluid. Emphasis is put on the different types of emerging instability, and how they may be related to the description of turbulence.

On a Relaxation Approximation of the Incompressible Navier-stokes Equations

Integrable Structures for 2D Euler Equations of Incompressible Inviscid Fluids

The governing equation of turbulence, that we are interested in, is the incompressible 2D Navier– Stokes equation under periodic boundary conditions. We are particularly interested in investigating the dynamics of 2D Navier–Stokes equation in the infinite Reynolds number limit and of 2D Euler equation. Our approach is different from many other studies on 2D Navier–Stokes equation in which one s...

A Third-degree B-spline Collocation Scheme for Solving a Class of the Nonlinear Lane–-Emden Type Equations

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...

Improved Accuracy of Incompressible Approximation of Compressible Euler Equations

This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is O , where denotes the Mach number. In this article, however, we prove an O 2 accuracy for the incompressible approximation of the isentropic, compressible Euler equations thanks to several d...