Small Scales in the Navier-Stokes Equations

纳维-斯托克斯方程中的小尺度

• 批准号: 0072662
• 负责人: Igor Kukavica
• 金额: $ 9.35万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-15 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072662&HistoricalAwards=false
• 关键词: Small; Scales; Navier; Stokes; Equations

0072662KukavicaThis project will address definition, interplay, and rigorous estimates of various natural small scales arising in a viscous incompressible flow. In particular, we will consider those lengths that can be derived directly from solutions of the Navier-Stokes equations, which is the main model for a fluid flow. Examples of such scales are the those resulting from the Fourier spectrum of solutions, such as the inverse of the wave number at which the Fourier spectrum is cut off exponentially, and the length scales measuring complexity of level sets of solutions. Related problems will be addressed also for other dissipative partial differential equations arising in fluid dynamics, such as the Ginzburg-Landau and the Kuramoto-Sivashinsky equations.Navier-Stokes equations are perhaps the most widely studied system of nonlinear partial differential equations. They are generally believed to contain necessary ingredients to explain much of turbulence phenomena. This project will address properties of solutions which would have implications in understanding creation and properties of fine structures in a flow. Potential applications include quantifying complexity of a fluid flow, establishment of spectral properties of solutions, estimation of the size of the mesh needed to resolve a flow numerically, and information on locating observables for the flow's monitoring

[00:72662] kukavica这个项目将解决粘性不可压缩流中产生的各种自然小尺度的定义、相互作用和严格估计。特别是，我们将考虑那些可以直接从流体流动的主要模型Navier-Stokes方程的解中导出的长度。这种尺度的例子是由解的傅里叶谱产生的，例如傅里叶谱被指数切断的波数的倒数，以及测量解的水平集复杂性的长度尺度。本文还将讨论流体动力学中出现的其他耗散偏微分方程的相关问题，如金兹堡-朗道方程和Kuramoto-Sivashinsky方程。Navier-Stokes方程可能是研究最广泛的非线性偏微分方程组。它们通常被认为包含了解释许多湍流现象的必要成分。这个项目将讨论解决方案的性质，这将对理解流中精细结构的产生和性质产生影响。潜在的应用包括量化流体流动的复杂性，建立溶液的光谱特性，估计流体流动所需的网格大小，以及为流动监测定位可观测物的信息