Mathematical Questions in Kinetic Theory

动力学理论中的数学问题

• 批准号: 2054726
• 负责人: Toan Nguyen
• 金额: $ 30万
• 依托单位: Pennsylvania State Univ University Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2054726&HistoricalAwards=false
• 关键词: Mathematical; Questions; Kinetic; Theory

This research project will address fundamental problems concerning solutions to partial differential equations that are used to model the dynamics of plasmas and fluids in physics. The focus will be on studying the fundamental law of physics to predict mixing and relaxation of macroscopic quantities in the large time. The project will contribute new mathematical techniques to the theory of partial differential equations and the field of mathematical physics, dynamical systems, and applied mathematics. In addition, it will advance our understanding of turbulence in plasma physics and fluid dynamics. The project provides training opportunities for graduate students and other early-career researchers. The project seeks to advance beyond the study of mixing and relaxation, or Landau damping, in plasma physics and fluid dynamics, and to address fundamental stability problems concerning the behavior of solutions with limited regularity. The fundamental equations to be studied include the classical Vlasov models in plasma physics and the Euler and Navier-Stokes equations in fluid dynamics. The goal is to provide new insights into Landau damping and mixing in plasmas and fluids. The main approaches will involve mathematical techniques from spectral theory, resolvent analysis, Fourier analysis, dispersive PDEs, probability, and statistical physics.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.

该研究项目将解决有关偏微分方程解决方案解决方案的基本问题，这些方程用于建模物理学中的等离子体和流体的动力学。重点将放在研究物理学的基本定律上，以预测大量宏观量的混合和放松。该项目将为部分微分方程以及数学物理，动力学系统和应用数学的领域贡献新的数学技术。此外，它将提高我们对等离子体物理和流体动力学湍流的理解。该项目为研究生和其他早期研究人员提供了培训机会。该项目旨在超越血浆物理和流体动力学的混合和放松或Landau阻尼的研究，并解决有关解决方案行为的基本稳定性问题，以有限的规律性。要研究的基本方程包括等离子体物理学中的经典vlasov模型以及流体动力学中的Euler和Navier-Stokes方程。目的是为血浆和流体中的Landau阻尼和混合提供新的见解。主要方法将涉及光谱理论，解决分析，傅立叶分析，分散PDE，概率和统计物理学的数学技术。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来获得支持的。

项目成果

The inviscid limit for the 2D Navier-Stokes equations in bounded domains

• DOI: 10.3934/krm.2022004
• 发表时间: 2021-11
• 期刊: Kinetic & Related Models
• 影响因子: 1
• 作者: C. Bardos;Trinh T. Nguyen;Toan T. Nguyen;E. Titi