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Mathematical Questions in Classical and Relativistic Fluids and Applications

经典和相对论流体中的数学问题及其应用

基本信息

批准号：
1812826
负责人：
Marcelo Disconzi
金额：
$ 12万
依托单位：
Vanderbilt University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1812826&HistoricalAwards=false
关键词：
Mathematical Questions Classical Relativistic Fluids

项目摘要

Mathematical fluid dynamics investigates the mathematical properties of the equations employed to describe the motion of fluids. This subject has a long history but many important questions remain open. This project focuses on free-boundary problems for compressible flows and relativistic fluids. The atmosphere, stars, and gaseous planets can be described by compressible flows with a free surface. The equations of free-boundary fluids present many challenges and only recently we have begun to understand their mathematical properties. By relativistic fluids, one means fluids in a regime where Einstein's theory of relativity cannot be neglected. Neutron stars and quark-gluon plasma (an exotic state of matter that forms in heavy-ion collisions) can be described by viscous relativistic fluids. The equations of relativistic fluid dynamics present a rich mathematical structure that has been the source of intensive investigation in recent years.This project investigates a variety of problems in classical and relativistic fluids that are part of very active research areas. This project will investigate the free-boundary Euler equations, with focus on the case of compressible fluids, a subject much less developed than its incompressible counterpart. This project will investigate questions of existence, uniqueness, long-time behavior, the incompressible limit, and the role of surface tension and rotation in the flow. For relativistic fluids, the focus will be primarily in the case of fluids with viscosity. This is an area that has witnessed a great deal of activity in physics in recent years but whose mathematical foundations are underdeveloped. This project will contribute to put the theory of relativistic viscous fluids on a firm mathematical basis and use this knowledge to solve problems of direct relevance to 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.

数学流体动力学研究用来描述流体运动的方程的数学性质。这一课题由来已久，但许多重要问题仍然悬而未决。本项目主要研究可压缩流体和相对论流体的自由边界问题。大气、恒星和气态行星可以用具有自由表面的可压缩流动来描述。自由边界流体的方程提出了许多挑战，直到最近我们才开始了解它们的数学性质。所谓相对论流体，指的是处于爱因斯坦相对论不可忽视的状态下的流体。中子星和夸克-胶子等离子体(重离子碰撞中形成的物质的一种奇异状态)可以用粘性相对论流体来描述。相对论流体动力学方程呈现了丰富的数学结构，这是近年来深入研究的来源。这个项目研究了经典流体和相对论流体中的各种问题，这是非常活跃的研究领域的一部分。这个项目将研究自由边界欧拉方程，重点是可压缩流体的情况，这是一个比不可压缩流体要落后得多的学科。这个项目将研究存在、唯一性、长期行为、不可压缩极限以及表面张力和旋转在流动中的作用等问题。对于相对论流体，焦点将主要放在粘性流体的情况下。这是一个近年来在物理学中有大量活动的领域，但其数学基础还不发达。该项目将有助于将相对论粘性流体理论建立在坚实的数学基础上，并利用这一知识解决与物理直接相关的问题。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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

期刊论文数量（12）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

A priori estimates for the free-boundary Euler equations with surface tension in three dimensions

三维表面张力自由边界欧拉方程的先验估计

DOI：
10.1088/1361-6544/ab0b0d
发表时间：
2019
期刊：
Nonlinearity
影响因子：
1.7
作者：
Disconzi, Marcelo M;Kukavica, Igor
通讯作者：
Kukavica, Igor

Local existence and uniqueness in Sobolev spaces for first-order conformal causal relativistic viscous hydrodynamics

一阶共形因果相对论粘性流体动力学 Sobolev 空间中的局部存在性和唯一性

DOI：
10.3934/cpaa.2021069
发表时间：
2021
期刊：
Communications on Pure & Applied Analysis
影响因子：
1
作者：
Bemfica, Fabio Sperotto;Disconzi, Marcelo Mendes;Rodriguez, Casey;Shao, Yuanzhen
通讯作者：
Shao, Yuanzhen

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