Stabilizing Phenomenon for Incompressible Fluids

不可压缩流体的稳定现象

基本信息

  • 批准号:
    2104682
  • 负责人:
  • 金额:
    $ 26.7万
  • 依托单位:
  • 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:
    2021-06-01 至 2025-05-31
  • 项目状态:
    未结题

项目摘要

This project seeks to understand an important universal stabilizing phenomenon concerning several incompressible fluids. The magnetic field stabilizes and damps electrically conducting fluids, a phenomenon observed in many physical experiments and numerical simulations. The temperature tames and stabilizes buoyancy driven fluids and helps the formation of stable structures in turbulent thermal convection. These are just two outstanding examples of a universal stabilizing phenomenon. The goal of this project is to fully comprehend this remarkable phenomenon and establish these observations as mathematically rigorous stability results on the models governing the dynamics of these flows. Understanding the proposed stability problems will help gain insight into many astronomical and meteorological phenomena such as Northern lights, solar flares, and severe weather events. The PIs will integrate the proposed research with the training of graduate students. In addition, the PIs will host events to get more K-16 students interested in these mathematical topics.This project focuses on the stability and large-time dynamics of the magnetohydrodynamic (MHD) equations near a background magnetic field and on the Boussinesq equations near the hydrostatic equilibrium. Mathematically these are extremely difficult problems. The fluid velocity in these MHD and Boussinesq systems is governed by the Euler or the Euler-like equations. The corresponding vorticity gradients could potentially grow rather rapidly in time. This makes the proposed stability problems appear to be impossible. The goal here is to solve these difficult problems by creating new strategies and innovative approaches. In particular, the PIs will reverse some of the classical approaches to the global regularity and stability problems on the MHD and the Boussinesq equations and treat the bad terms such as the Lorentz force and the buoyancy force in these models as good terms and exploit the smoothing and stabilizing effect of the magnetic field and the temperature. In addition, extensive numerical simulations will be performed to complement the theoretical studies.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.
这个项目旨在了解一个重要的普遍稳定现象,涉及几个不可压缩流体。磁场稳定和阻尼导电流体,这是许多物理实验和数值模拟中观察到的现象。温度驯服和稳定浮力驱动的流体,并有助于在湍流热对流中形成稳定的结构。这只是普遍稳定现象的两个突出例子。该项目的目标是充分理解这一显着的现象,并建立这些观测作为数学上严格的稳定性结果的模型,这些流动的动力学。了解所提出的稳定性问题将有助于深入了解许多天文和气象现象,如北方光,太阳耀斑和恶劣的天气事件。PI将把拟议的研究与研究生的培训结合起来。此外,PI将举办活动,让更多的K-16学生对这些数学主题感兴趣。这个项目的重点是在背景磁场附近的磁流体动力学(MHD)方程的稳定性和大时间动力学,以及在流体静力平衡附近的Boussinesq方程。在数学上,这些都是非常困难的问题。这些MHD和Boussinesq系统中的流体速度由欧拉或类欧拉方程控制。相应的涡度梯度可能会随着时间的推移而相当迅速地增长。这使得所提出的稳定性问题似乎是不可能的。我们的目标是通过制定新的战略和创新方法来解决这些难题。特别是,PI将扭转一些经典的方法来解决MHD和Boussinesq方程的全局正则性和稳定性问题,并将这些模型中的洛仑兹力和浮力等不良项视为良好项,并利用磁场和温度的平滑和稳定效果。 此外,将进行广泛的数值模拟,以补充理论研究。该奖项反映了NSF的法定使命,并已被认为是值得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的支持。

项目成果

期刊论文数量(14)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Global well-posedness for 2D non-resistive compressible MHD system in periodic domain
  • DOI:
    10.1016/j.jfa.2022.109602
  • 发表时间:
    2022-06
  • 期刊:
  • 影响因子:
    1.7
  • 作者:
    Jiahong Wu;Yi Zhu
  • 通讯作者:
    Jiahong Wu;Yi Zhu
Stability of Couette flow for 2D Boussinesq system with vertical dissipation
  • DOI:
    10.1016/j.jfa.2021.109255
  • 发表时间:
    2020-04
  • 期刊:
  • 影响因子:
    1.7
  • 作者:
    Wen Deng;Jiahong Wu;Ping Zhang
  • 通讯作者:
    Wen Deng;Jiahong Wu;Ping Zhang
Stability and large-time behavior for the 2D Boussineq system with horizontal dissipation and vertical thermal diffusion
  • DOI:
    10.1007/s00030-022-00773-4
  • 发表时间:
    2022-05
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Dhanapati Adhikari;Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
  • 通讯作者:
    Dhanapati Adhikari;Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
The stabilizing effect of the temperature on buoyancy-driven fluids
  • DOI:
    10.1512/iumj.2022.71.9070
  • 发表时间:
    2020-05
  • 期刊:
  • 影响因子:
    1.1
  • 作者:
    Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
  • 通讯作者:
    Oussama Ben Said;Uddhaba Raj Pandey;Jiahong Wu
Global Solutions to 3D Incompressible MHD System with Dissipation in Only One Direction
  • DOI:
    10.1137/22m1471274
  • 发表时间:
    2022-10
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Hongxia Lin;Jiahong Wu;Yi Zhu
  • 通讯作者:
    Hongxia Lin;Jiahong Wu;Yi Zhu
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Jiahong Wu其他文献

Stabilization of a Background Magnetic Field on a 2 Dimensional Magnetohydrodynamic Flow
二维磁流体动力流背景磁场的稳定
Analytic results related to magneto-hydrodynamic turbulence
  • DOI:
    10.1016/s0167-2789(99)00158-x
  • 发表时间:
    2000-02
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Jiahong Wu
  • 通讯作者:
    Jiahong Wu
Boundary Control for Optimal Mixing via Navier-Stokes Flows
通过纳维-斯托克斯流实现最佳混合的边界控制
Unique weak solutions of the non-resistive magnetohydrodynamic equations with fractional dissipation
具有分数耗散的非电阻磁流体动力学方程的独特弱解
  • DOI:
    10.4310/cms.2020.v18.n4.a5
  • 发表时间:
    2019-04
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Quansen Jiu;Xiaoxiao Suo;Jiahong Wu;Huan Yu
  • 通讯作者:
    Huan Yu
Well-posedness of the two-dimensional generalized Benjamin-Bona-Mahony equation on the upper half plane
二维广义Benjamin-Bona-Mahony方程在上半平面上的适定性
  • DOI:
    10.3934/dcdsb.2016.21.763
  • 发表时间:
    2015
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Ying;C. H. A. Cheng;John M. Hong;Jiahong Wu;Juan
  • 通讯作者:
    Juan

Jiahong Wu的其他文献

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{{ truncateString('Jiahong Wu', 18)}}的其他基金

Collaborative Research: Effective Numerical Schemes for Fundamental Problems Related to Incompressible Fluids
合作研究:与不可压缩流体相关的基本问题的有效数值方案
  • 批准号:
    2309748
  • 财政年份:
    2023
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
Regularity Problem on Two Models from Fluid Dynamics
流体动力学两个模型的正则性问题
  • 批准号:
    1614246
  • 财政年份:
    2016
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
CBMS Conference: Regularity Problem for Partial Differential Equations Modeling Fluids and Geophysical Fluids
CBMS 会议:偏微分方程模拟流体和地球物理流体的正则性问题
  • 批准号:
    1342592
  • 财政年份:
    2014
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
The Fourth Oklahoma Partial Differential Equations (PDE) Workshop; Oklahoma State University; October 26-27, 2013
第四届俄克拉荷马州偏微分方程 (PDE) 研讨会;
  • 批准号:
    1338025
  • 财政年份:
    2013
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
Analysis and Applications of Two Partial Differential Equations Modeling Geophysical Fluids
模拟地球物理流体的两个偏微分方程的分析与应用
  • 批准号:
    1209153
  • 财政年份:
    2012
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
International Conference on Partial Differential Equations Modeling Fluids and Complex Fluids - Xi'an, China, June 2011
偏微分方程模拟流体和复杂流体国际会议 - 中国西安,2011 年 6 月
  • 批准号:
    1053163
  • 财政年份:
    2011
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
Collaborative Research: Oklahoma PDE and Applied Math Workshops
合作研究:俄克拉荷马州偏微分方程和应用数学研讨会
  • 批准号:
    1135402
  • 财政年份:
    2011
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
Oklahoma PDE Workshop; October 2009
俄克拉荷马州偏微分方程研讨会;
  • 批准号:
    0930845
  • 财政年份:
    2009
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant
Two Partial Differential Equations Modeling Geophysical Fluids
模拟地球物理流体的两个偏微分方程
  • 批准号:
    0907913
  • 财政年份:
    2009
  • 资助金额:
    $ 26.7万
  • 项目类别:
    Standard Grant

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