Analytic Methods in Hydrodynamic and Wave Turbulence

流体动力学和波浪湍流的分析方法

• 批准号: 1900149
• 负责人: Tristan Buckmaster
• 金额: $ 20.07万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-09-01 至 2022-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900149&HistoricalAwards=false
• 关键词: Analytic; Methods; Hydrodynamic; Wave; Turbulence

Turbulence is ubiquitous in nature, playing a fundamental role in a multitude of physical theories, from atmospheric and oceanic dynamics to the birth of stars. This project is dedicated to an investigation into hydrodynamic and wave turbulence, both of which, at the core predict cascades of energy. The principal aim of this supported research is to better understand these energy cascades. The project is divided into two projects: a study of non-uniqueness of weak solutions to equations arising in hydrodynamics, and a rigorous approach to the derivation of the kinetic wave equation in wave turbulence theory. The focus of the first project will be to utilize the theoretical tool of convex integration to build theoretical energy cascades in order to resolve long standing open problems related to weak solutions to the Navier-Stokes equations. The overarching goal of the second project will be to rigorously determine the validity of the kinetic wave equation which is theorized to predict turbulence phenomena in a host settings such as water waves, plasma physics and climate science. The project will draw on a diverse set of mathematical tools from analysis, number theory 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.

湍流在自然界中无处不在，从大气和海洋动力学到恒星的诞生，在许多物理理论中发挥着重要作用。该项目致力于研究水动力学和波浪湍流，两者的核心都是预测能量的级联。这项研究的主要目的是更好地了解这些能量级联。该项目分为两个项目：研究流体力学方程弱解的非唯一性，以及波浪湍流理论中动力波方程推导的严格方法。 第一个项目的重点将是利用凸积分的理论工具来建立理论能量级联，以解决与纳维-斯托克斯方程弱解有关的长期未决问题。第二个项目的首要目标是严格确定动力波方程的有效性，该方程被理论化以预测水波、等离子体物理学和气候科学等主机环境中的湍流现象。这个奖项反映了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

A Heuristic Approach to Convex Integration for the Euler Equations

欧拉方程凸积分的启发式方法

• DOI: 10.1007/978-3-030-54899-5_1
• 发表时间: 2020
• 期刊: Lecture notes in mathematics
• 作者: Buckmaster, Tristan;Vicol, Vlad
• 通讯作者: Vicol, Vlad

Convex integration constructions in hydrodynamics

• DOI: 10.1090/bull/1713
• 发表时间: 2020-11
• 期刊: Bulletin of the American Mathematical Society
• 影响因子: 1.3
• 作者: T. Buckmaster;V. Vicol

On the kinetic wave turbulence description for NLS

NLS的动波湍流描述

• DOI: 10.1090/qam/1554
• 发表时间: 2020
• 期刊: Quarterly of Applied Mathematics
• 影响因子: 0.8
• 作者: Buckmaster, T.;Germain, P.;Hani, Z.;Shatah, J.
• 通讯作者: Shatah, J.

Convex integration and phenomenologies in turbulence

• DOI: 10.4171/emss/34
• 发表时间: 2019-01-01
• 期刊: EMS SURVEYS IN MATHEMATICAL SCIENCES
• 影响因子: 2.3
• 作者: Buckmaster, Tristan;Vicol, Vlad
• 通讯作者: Vicol, Vlad

Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation

非线性薛定谔方程长期行为的波湍流描述

• DOI: 10.1007/s00222-021-01039-z
• 发表时间: 2021
• 期刊: Inventiones mathematicae
• 影响因子: 3.1
• 作者: Buckmaster, T.;Germain, P.;Hani, Z.;Shatah, J.
• 通讯作者: Shatah, J.