The Inviscid Limit and Large Time Behavior of Fluid Flows

流体流动的无粘极限和长时间行为

• 批准号: 1764119
• 负责人: Toan Nguyen
• 金额: $ 21万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-05-01 至 2022-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1764119&HistoricalAwards=false
• 关键词: Inviscid; Limit; Large; Time; Behavior

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.

这个研究项目研究流体的运动，如水或空气流过固体物体，如船或机翼。一个特别的重点将是研究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描述流体运动，涉及几个不同长度尺度的薄层，并更好地了解从层流到湍流的过渡。该研究将有助于更好地计算翼型表面摩擦阻力以及物体与周围流体之间的热传递。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，在具有边界的区域中构造了具有小粘性的经典Navier-Stokes方程的多层解，并研究了大时间内流体流动的阻尼机制。目的是阐明粘性边界层的新认识。主要的方法将涉及谱分析和预解估计的线性化Navier-Stokes方程附近的一般剪切流。流体阻尼的研究将利用色散方程和量子理论改编的技术。该奖项反映了NSF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。

项目成果

Onsager-type conjecture and renormalized solutions for the relativistic Vlasov–Maxwell system

• DOI: 10.1090/qam/1549
• 发表时间: 2019-03
• 期刊: Quarterly of Applied Mathematics
• 影响因子: 0.8
• 作者: C. Bardos;N. Besse;Toan T. Nguyen

On the Linearized Vlasov–Poisson System on the Whole Space Around Stable Homogeneous Equilibria

关于稳定齐次平衡全空间上的线性化Vlasov-Poisson系统

• DOI: 10.1007/s00220-021-04228-2
• 发表时间: 2021
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: Han-Kwan, Daniel;Nguyen, Toan T.;Rousset, Frédéric
• 通讯作者: Rousset, Frédéric

Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates

通过逐点色散估计筛选 Vlasov-Poisson 系统平衡点的渐近稳定性

• DOI: 10.1007/s40818-021-00110-5
• 发表时间: 2021
• 期刊: Annals of PDE
• 影响因子: 2.8
• 作者: Han-Kwan, Daniel;Nguyen, Toan T.;Rousset, Frédéric
• 通讯作者: Rousset, Frédéric

Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria

围绕彭罗斯稳定平衡筛选的弗拉索夫-泊松系统的导数估计

• DOI: 10.3934/krm.2020043
• 发表时间: 2020
• 期刊: Kinetic & Related Models
• 影响因子: 1
• 作者: T. Nguyen, Trinh

On Global Stability of Optimal Rearrangement Maps

论最优重排图的全局稳定性

• DOI: 10.1007/s00205-020-01552-0
• 发表时间: 2020
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: Nguyen, Huy Q.;Nguyen, Toan T.
• 通讯作者: Nguyen, Toan T.