Convex integration constructions in hydrodynamics
Convex integration constructions in hydrodynamics
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DOI：
10.1090/bull/1713
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发表时间：
2020-11
影响因子：
1.3
通讯作者：
T. Buckmaster;V. Vicol
中科院分区：
文献类型：
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作者：
T. Buckmaster;V. Vicol
.我们回顾了最近的发展领域的数学流体动力学，利用技术，在伞下的名称凸积分。在流体动力学的背景下，这些方法产生矛盾的解决方案，违反物理定律的流体方程。这些反直觉的解有许多类似于唯象学理论对流体湍流的预测的性质。这篇评论的目的是强调其中的一些相似之处，同时强调严格的数学陈述。我们的注意力集中在不可压缩的欧拉方程，Navier-Stokes方程和磁流体动力学方程，违反这些系统的物理能量定律的弱解的建设。
. We review recent developments in the field of mathematical fluid dynamics which utilize techniques that go under the umbrella name convex integration . In the hydrodynamical context, these methods produce paradoxical solutions to the fluid equations which defy physical laws. These counter-intuitive solutions have a number of properties that resemble predictions made by phenomenological theories of fluid turbulence. The goal of this review is to highlight some of these similarities while maintaining an emphasis on rigorous mathematical statements. We focus our attention on the construction of weak solutions for the incompressible Euler, Navier–Stokes, and magneto-hydrodynamic equations which violate these systems’ physical energy laws.