Mathematical Theory of Incompressible Nonviscous Fluids
Mathematical Theory of Incompressible Nonviscous Fluids
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DOI：
10.1007/978-1-4612-4284-0
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发表时间：
1993-11
期刊：
影响因子：
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通讯作者：
C. Marchioro;M. Pulvirenti
中科院分区：
文献类型：
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作者：
C. Marchioro;M. Pulvirenti
流体动力学是一门古老的科学，今天仍然非常活跃。现代技术和新的需求要求对真实的流体的行为有更深入的了解，新的发现或进展常常提出具有挑战性和困难的新数学问题。在这个框架中，不可压缩的非粘性（有时称为理想）流起着特殊的作用。这是一个数学模型，基本上由流体速度场的演化方程（欧拉方程）组成。这样一个方程，它只不过是牛顿定律加上一些附加的结构假设，是欧拉在1755年发现的，虽然它已经有两个多世纪的历史了，但关于它的解的许多基本问题仍然是开放的。特别是，它是不知道的解决方案，合理的一般初始条件下，在有限的时间内发展奇点，很少有人知道光滑的解决方案的长期行为。这些问题和其他一些基本问题仍然没有解决，这也是完全流的数学理论远未完成的原因之一。不可压缩流已经被许多杰出的数学家用各种各样的数学方法加以研究，因此，今天，这一领域构成了应用数学中非常丰富和令人振奋的一部分。
Fluid dynamics is an ancient science incredibly alive today. Modern technol ogy and new needs require a deeper knowledge of the behavior of real fluids, and new discoveries or steps forward pose, quite often, challenging and diffi cult new mathematical {:: oblems. In this framework, a special role is played by incompressible nonviscous (sometimes called perfect) flows. This is a mathematical model consisting essentially of an evolution equation (the Euler equation) for the velocity field of fluids. Such an equation, which is nothing other than the Newton laws plus some additional structural hypo theses, was discovered by Euler in 1755, and although it is more than two centuries old, many fundamental questions concerning its solutions are still open. In particular, it is not known whether the solutions, for reasonably general initial conditions, develop singularities in a finite time, and very little is known about the long-term behavior of smooth solutions. These and other basic problems are still open, and this is one of the reasons why the mathe matical theory of perfect flows is far from being completed. Incompressible flows have been attached, by many distinguished mathe maticians, with a large variety of mathematical techniques so that, today, this field constitutes a very rich and stimulating part of applied mathematics.