The Inviscid Limit and Large Time Behavior of Fluid Flows

这个研究项目研究流体（如水或空气）流过固体物体（如船或机翼）时的运动。一个特别的重点将是研究在固体物体表面附近出现的薄层。这项研究将提供一个更准确的流体运动描述，包括几个不同长度尺度的薄层，并更好地理解从层流到湍流的转变。这项研究将有助于更好地计算翼型的表面摩擦阻力和物体与周围流体之间的热量传递。该项目将包括培养研究生的研究活动。该项目证明了一般边界层的不稳定性，构建了具有边界域的经典小粘度Navier-Stokes方程的多层解，并研究了大时间内流体流动的阻尼机理。目的是阐明对粘性边界层的新认识。主要方法包括谱分析和一般剪切流附近线性化Navier-Stokes方程的解析估计。流体阻尼的研究将利用从色散方程和量子理论改编的技术。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This research project studies the motion of fluids such as water or air moving past solid objects such as a ship or an airfoil. A particular focus will be on studying the thin layers that emerge near the surface of solid objects. The research will provide a more accurate description of the fluid motion that involves several thin layers with different length scales and a better understanding of the transition from laminar to turbulent flows. The study will help to better calculate the skin friction drag on an airfoil and the heat transfer between a body and the fluid around it. The project will include research activities that train graduate students. The project proves the instability of generic boundary layers, constructs multi-layer solutions to classical Navier-Stokes equations with small viscosity in domains with a boundary, and studies the damping mechanism of fluid flows at the large time. The goal is to elucidate the new understanding of viscous boundary layers. The main approach will involve the spectral analysis and resolvent estimates of linearized Navier-Stokes equations near generic shear flows. The study of fluid damping will make use of techniques that are adapted from dispersive equations and quantum theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.