Scale-dependent Error Growth in Navier--Stokes Simulations

Reinterpreting Shock Wave Structure Predictions using the Navier-Stokes Equations

Classical Navier-Stokes equations fail to predict shock wave profiles accurately. In this paper, the Navier-Stokes system is fully transformed using a velocity variable transformation. The transformed equations termed the re-casted Navier-Stokes equations display physics not initially included. We then analyse the stationary shock structure problem in a monatomic gas by solving both the classical and the re-casted Navier-Stokes equations numerically using a finite difference global solution (FDGS) scheme. The numerical results are presented for different upstream Mach numbers ranging from supe…

Navier-Stokes方程组的时间离散解法

On a time-discrete approach to solving Navier-Stokes systems

提出了一种求解Navier-Stokes方程组的新格式。这是灵感来自材料差异化和离散莫尔斯半流相结合。该解存在第一个能量不等式，但我们做了一些假设。这个结果并没有提供任何新的结果，但我相信，通过使我的方案更复杂，我们可以发展Navier-Stokes系统的研究。

纳维-斯托克斯方程的对称约化和精确解

Symmetry reduction and exact solutions of the Navier-Stokes equations

本文描述了Navier-Stokes场的几种形式。这些解将纳维-斯托克斯方程化为三个、两个和一个独立变量的微分方程组。构造了纳维-斯托克斯方程的大量精确解。

考虑几何效应的Euler和Navier-Stokes方程斯托克斯方程的严格证明

A rigorous justification of the Euler and Navier-Stokes equations with geometric effects

本文导出了描述气体通过变截面喷管运动的一维等熵Euler方程和斯托克斯方程，作为三维等熵Navier-Stokes方程组在直径趋于零的圆柱中的渐近极限。我们的方法是基于相对能量不等式满足的任何弱解的三维Navier-Stokes系统和变形的Korn-Poincare不等式薄通道，可能是独立的利益。

刚性和可膨胀管道和网络中Poiffille流与一维Navier-Stokes流的比较

Comparing Poiseuille with 1D Navier-Stokes Flow in Rigid and Distensible Tubes and Networks

本文对刚性管和网络中的Hagen-Poiffille流与弹性管和网络中的一维N-S流进行了比较。分析关系，Poiffille网络流动模型和两个有限元Navier-Stokes一维流动模型已被开发并用于这项调查。比较突出了Poiffille和一维Navier-Stokes流动模型之间的差异，这些模型在某些研究中可能被不可解释地视为等效模型。

Quotients of Navier--Stokes equation on space curves

A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial expansion of the Planck potential, we reduce the quotient equation to a series of systems of ordinary differential equations.

Navier-Stokes方程的Reynolds平均解

Reynolds Averaged Solutions of the Navier-Stokes Equation

本文证明一般初始条件下Navier-Stokes方程Young测度解的均值属于Leray-Hopf类PDE解。

Multi-dimensional Jordan chain and Navier-Stokes Equation

Multi-dimensional Jordan chain is presented. It is shown that it admits the finite-component reductions to the Navier-Stokes equation and other important equations of continuous media theory.

Some preliminary observations on a defect Navier-Stokes system

Some implications of the simplest accounting of defects of compatibility in the velocity field on the structure of the classical Navier-Stokes equations are explored, leading to connections between classical elasticity, the elastic theory of defects, plasticity theory, and classical fluid mechanics.

Geometric Regularity Criteria for Incompressible Navier--Stokes Equations with Navier Boundary Conditions

We study the regularity criteria for weak solutions to the $3D$ incompressible Navier--Stokes equations in terms of the geometry of vortex structures, taking into account the boundary effects. A boundary regularity theorem is proved on regular domains with a class of oblique derivative boundary conditions, providing that the vorticity of the fluid is coherently aligned. In particular, we establish the boundary regularity on round balls, half-spaces and right circular cylindrical ducts, subject to the classical Navier and kinematic boundary conditions.