Regularity, Stability, and Turbulence in Fluid Flows

流体流动的规律性、稳定性和湍流

• 批准号: 1907981
• 负责人: Alexis Vasseur
• 金额: $ 29.89万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907981&HistoricalAwards=false
• 关键词: Regularity; Stability; Turbulence; Fluid; Flows

This project will advance the knowledge of physical models which are of fundamental importance in engineering, meteorology, or natural disaster, such as flooding and hurricanes. It will advance the development of powerful mathematical tools based on state of the art analysis, and the theory of linear and nonlinear partial differential equations. An important component of the project concerns the training and mentoring of a new generation of scientists and researchers. The research program provides ample opportunities for Ph.D. students and Postdocs to be trained in mathematical analysis and physical modeling applied to fluid mechanics. This project uses powerful mathematical tools to tackle several fundamental questions on the behavior of flows in fluid mechanic. A rigorous theory will be developed to study how incompressible flows become linearly unstable close to possible blow-up time, a typical signature of turbulence. The effect of boundaries on the dynamic of incompressible flows is of paramount importance. It will be thoroughly investigated on the 3D quasi-geostrophic equation, a model used in meteorology and oceanography.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.

该项目将增进对物理模型的了解，这些模型在工程、气象学或洪水和飓风等自然灾害中具有根本重要性。它将推动基于最先进的分析以及线性和非线性偏微分方程理论的强大数学工具的开发。该项目的一个重要组成部分涉及新一代科学家和研究人员的培训和指导。该研究计划为博士学位提供了充足的机会。学生和博士后接受流体力学数学分析和物理建模方面的培训。该项目使用强大的数学工具来解决流体力学中流动行为的几个基本问​​题。将开发一个严格的理论来研究不可压缩流如何在接近可能的爆炸时间（湍流的典型特征）时变得线性不稳定。边界对不可压缩流动力学的影响至关重要。它将对 3D 准地转方程（一种用于气象学和海洋学的模型）进行彻底研究。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力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

Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics

气体动力学等熵系统的一组密集初始数据的全局不适定性

• DOI: 10.1016/j.aim.2021.108057
• 发表时间: 2021
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Chen, Robin Ming;Vasseur, Alexis F.;Yu, Cheng
• 通讯作者: Yu, Cheng

Uniqueness and Weak-BV Stability for $$2\times 2$$ Conservation Laws

$$2 imes 2$$ 守恒定律的唯一性和弱 BV 稳定性

• DOI: 10.1007/s00205-022-01813-0
• 发表时间: 2022
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: Chen, Geng;Krupa, Sam G.;Vasseur, Alexis F.
• 通讯作者: Vasseur, Alexis F.

Boundary Vorticity Estimates for Navier–Stokes and Application to the Inviscid Limit

纳维斯托克斯的边界涡估计及其对无粘极限的应用

• DOI: 10.1137/22m1503567
• 发表时间: 2023
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Vasseur, Alexis F.;Yang, Jincheng
• 通讯作者: Yang, Jincheng

Second Derivatives Estimate of Suitable Solutions to the 3D Navier–Stokes Equations

3D 纳维斯托克斯方程合适解的二阶导数估计

• DOI: 10.1007/s00205-021-01661-4
• 发表时间: 2021
• 期刊: Archive for Rational Mechanics and Analysis
• 影响因子: 2.5
• 作者: Vasseur, Alexis;Yang, Jincheng
• 通讯作者: Yang, Jincheng

Time-asymptotic stability of composite waves of viscous shock and rarefaction for barotropic Navier-Stokes equations

• DOI: 10.1016/j.aim.2023.108963
• 发表时间: 2021-04
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Moon-Jin Kang;A. Vasseur;Yi Wang