Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space
Existence and Smoothness of the Navier-Stokes Equation in Two and Three-Dimensional Euclidean Space
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DOI：
10.4172/2090-0902.1000167
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发表时间：
2016-05
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影响因子：
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通讯作者：
Tim Tarver
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文献类型：
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作者：
Tim Tarver
这个问题的解决方案多年来一直是未知的，而且它还没有解决的事实留下了许多关于工程和纯数学的未解问题。湍流是流体力学中的一个特定主题，当涉及到现实生活情况时，它是课程的重要组成部分。在二维和三维方程组和某些初始条件下，如果光滑解存在，则它们具有有界的动能。在三维空间和时间中，给定一个初始速度矢量，存在求解Navier-Stokes方程的光滑且全局定义的速度场和标量压力场。在二维和三维的可能解决方案中存在困难，并且长期没有解决，我们的目标是在三维中提出解决方案。我们看看能不能把几门纯数学课程联系起来得出一个结论。
A solution to this problem has been unknown for years and the fact that it hasn’t been solved yet leaves a lot of unanswered questions regarding Engineering and Pure Mathematics. Turbulence is a specific topic in fluid mechanics which is a vital part of the course when it comes to real life situations. In two and three dimensional systems of equations and some initial conditions, if the smooth solutions exist, they have bounded kinetic energy. In three space dimensions and time, given an initial velocity vector, there exists a velocity field and scalar pressure field which are both smooth and globally defined that solve the Navier-Stokes equations. There are difficulties in two-dimensions and three dimensions in a possible solution and which have been unsolved for a long time and our goal is to propose a solution in three-dimensions. Lets see if we can relate a couple of courses of pure mathematics to come up with an implication.