Qualitative Properties of Solutions to Fluids Equations

流体方程解的定性性质

• 批准号: 1907992
• 负责人: Igor Kukavica
• 金额: $ 27万
• 依托单位: University of Southern California
• 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: 2019-07-15 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907992&HistoricalAwards=false
• 关键词: Qualitative; Properties; Solutions; Fluids; Equations

This project addresses the solutions of partial differential equations modeling fluids. The principal goal is understanding the evolution of an incompressible fluid. In particular, the PI will study physical problems involving fluids with a free interface. This includes the motion of water waves, with or without surface tension, and a fluid-structure interaction problem. The PI will introduce techniques which shall advance our knowledge of fluids and promote further applications in science and engineering. Graduate students will be involved in all aspects of the project.For the fluid structure interaction system, the research will seek a priori estimates leading to the local and long-time existence of solutions and the construction of solutions satisfying these properties. The PI will also study the qualitative properties of solutions, such as the persistence of analytic and Sobolev regularity, along with asymptotic behavior. Furthermore, the research seeks to answer similar questions for the solutions of the Euler equations with a free interface, focusing on the local existence and uniqueness of solutions. The PI will work on properties of solutions of other important models in connection with fluid dynamics, such as the 2D and 3D Boussinesq equations, active scalar equations, and the Prandtl equations.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.

本计画探讨流体偏微分方程式之解。主要目标是了解不可压缩流体的演化。特别是，PI将研究涉及自由界面流体的物理问题。这包括水波的运动，有或没有表面张力，以及流体-结构相互作用问题。PI将介绍技术，这将促进我们对流体的认识，并促进在科学和工程中的进一步应用。研究生将参与项目的各个方面，对于流固耦合系统，研究将寻求导致解的局部和长期存在性的先验估计，并构造满足这些性质的解。PI还将研究解决方案的定性性质，如解析和Sobolev正则性的持久性，沿着渐近行为。此外，本文还研究了具有自由界面的Euler方程解的局部存在唯一性问题。PI将研究与流体动力学相关的其他重要模型的解的性质，如二维和三维Boussinesq方程、活动标量方程和Prandtl方程。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

Asymptotic properties of the Boussinesq equations with Dirichlet boundary conditions

• DOI: 10.3934/dcds.2023040
• 发表时间: 2021-09
• 期刊: Discrete and Continuous Dynamical Systems
• 影响因子: 1.1
• 作者: I. Kukavica;David Massatt;M. Ziane

Mach limits in analytic spaces

分析空间中的马赫极限

• DOI: 10.1016/j.jde.2021.07.014
• 发表时间: 2021
• 期刊: Journal of Differential Equations
• 影响因子: 2.4
• 作者: Jang, Juhi;Kukavica, Igor;Li, Linfeng
• 通讯作者: Li, Linfeng

A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension

具有表面张力的不可压缩自由边界欧拉方程的拉格朗日内正则结果

• DOI: 10.1137/18m1216808
• 发表时间: 2019
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Disconzi, Marcelo M.;Kukavica, Igor;Tuffaha, Amjad
• 通讯作者: Tuffaha, Amjad

Existence of global weak solutions to the Navier-Stokes equations in weighted spaces

加权空间中纳维-斯托克斯方程全局弱解的存在性

• DOI: 10.1512/iumj.2022.71.8789
• 发表时间: 2022
• 期刊: Indiana University Mathematics Journal
• 影响因子: 1.1
• 作者: Bradshaw, Zachary;Kukavica, Igor;Tsai, Tai-Peng
• 通讯作者: Tsai, Tai-Peng

Global Sobolev persistence for the fractional Boussinesq equation with zero diffusivity

零扩散率分数 Boussinesq 方程的全局 Sobolev 持久性

• 发表时间: 2020
• 期刊: Pure and applied functional analysis
• 作者: Kukavica, Igor;Wang, Weinan
• 通讯作者: Wang, Weinan