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了用于描述流体运动的方程式的数学特性。该主题的历史悠久，但许多重要的问题仍然开放。该项目着重于可压缩流和相对论流体的自由边界问题。可以通过自由表面的可压缩流来描述大气，恒星和气态行星。自由液体的方程式提出了许多挑战，直到最近我们才开始了解它们的数学特性。通过相对论的流体，意味着在爱因斯坦相对论无法忽视的政权中流体。可以用粘性相对论流体来描述中子星和夸克 - 杜松等离子体（在重离子碰撞中形成的异国情调状态）。相对论流体动力学的方程式呈现出丰富的数学结构，近年来一直是深入研究的来源。该项目研究了经典和相对论流体的各种问题，这些问题是非常活跃的研究领域的一部分。该项目将调查自由边缘的Euler方程，重点是可压缩流体的情况，该主题比其不可压缩的对应物要低得多。该项目将调查存在，独特性，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的问题。对于相对论流体，重点将主要是在具有粘度的流体的情况下。近年来，这个领域已经见证了物理学的大量活动，但其数学基础却欠发达。该项目将有助于将相对论粘性流体的理论牢固地数学，并利用这些知识来解决与物理学直接相关的问题。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和广泛的审查标准通过评估来通过评估来支持的。

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